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mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sl.wikipedia.org&uselang=sl" class=""><span>Denarni prispevki</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Posebno:Registracija&returnto=Izrek+o+povpre%C4%8Dni+vrednosti" title="Predlagamo vam, da si ustvarite račun in se prijavite, vendar to ni obvezno." class=""><span>Ustvari račun</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Posebno:Prijava&returnto=Izrek+o+povpre%C4%8Dni+vrednosti" title="Prijava je zaželena, vendar ni 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stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Uvod</div> </a> </li> <li id="toc-Formalna_izjava" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formalna_izjava"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Formalna izjava</span> </div> </a> <ul id="toc-Formalna_izjava-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Vsebina" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Vklopi kazalo vsebine" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Vklopi kazalo vsebine</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Izrek o povprečni vrednosti</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="P9jdi na članek v drugem jeziku. Na voljo v 52 jezikih." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-52" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">52 jezikov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%9B%E1%8B%95%E1%8A%A8%E1%88%8B%E1%8B%8A_%E1%8B%8B%E1%8C%8B_%E1%8A%A5%E1%88%AD%E1%8C%8D%E1%8C%A5" title="ማዕከላዊ ዋጋ እርግጥ – amharščina" lang="am" hreflang="am" data-title="ማዕከላዊ ዋጋ እርግጥ" data-language-autonym="አማርኛ" data-language-local-name="amharščina" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%A8%D8%B1%D9%87%D9%86%D8%A9_%D8%A7%D9%84%D9%82%D9%8A%D9%85%D8%A9_%D8%A7%D9%84%D9%85%D8%AA%D9%88%D8%B3%D8%B7%D8%A9" title="مبرهنة القيمة المتوسطة – arabščina" lang="ar" hreflang="ar" data-title="مبرهنة القيمة المتوسطة" data-language-autonym="العربية" data-language-local-name="arabščina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Orta_qiym%C9%99t_teoremi" title="Orta qiymət teoremi – azerbajdžanščina" lang="az" hreflang="az" data-title="Orta qiymət teoremi" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanščina" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%A1%E0%A6%BC_%E0%A6%AE%E0%A6%BE%E0%A6%A8_%E0%A6%89%E0%A6%AA%E0%A6%AA%E0%A6%BE%E0%A6%A6%E0%A7%8D%E0%A6%AF" title="গড় মান উপপাদ্য – bengalščina" lang="bn" hreflang="bn" data-title="গড় মান উপপাদ্য" data-language-autonym="বাংলা" data-language-local-name="bengalščina" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teorema_del_valor_mitj%C3%A0" title="Teorema del valor mitjà – katalonščina" lang="ca" hreflang="ca" data-title="Teorema del valor mitjà" data-language-autonym="Català" data-language-local-name="katalonščina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8C%DB%86%D8%B1%D9%85%DB%8C_%D8%A8%DB%95%DA%BE%D8%A7%DB%8C_%D9%86%D8%A7%D9%88%DB%95%D9%86%D8%AF" title="تیۆرمی بەھای ناوەند – osrednja kurdščina" lang="ckb" hreflang="ckb" data-title="تیۆرمی بەھای ناوەند" data-language-autonym="کوردی" data-language-local-name="osrednja kurdščina" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/V%C4%9Bta_o_st%C5%99edn%C3%AD_hodnot%C4%9B_diferenci%C3%A1ln%C3%ADho_po%C4%8Dtu" title="Věta o střední hodnotě diferenciálního počtu – češčina" lang="cs" hreflang="cs" data-title="Věta o střední hodnotě diferenciálního počtu" data-language-autonym="Čeština" data-language-local-name="češčina" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Theorem_gwerth-cymedrig" title="Theorem gwerth-cymedrig – valižanščina" lang="cy" hreflang="cy" data-title="Theorem gwerth-cymedrig" data-language-autonym="Cymraeg" data-language-local-name="valižanščina" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Middelv%C3%A6rdis%C3%A6tningen" title="Middelværdisætningen – danščina" lang="da" hreflang="da" data-title="Middelværdisætningen" data-language-autonym="Dansk" data-language-local-name="danščina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Mittelwertsatz_der_Differentialrechnung" title="Mittelwertsatz der Differentialrechnung – nemščina" lang="de" hreflang="de" data-title="Mittelwertsatz der Differentialrechnung" data-language-autonym="Deutsch" data-language-local-name="nemščina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%98%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1_%CE%BC%CE%AD%CF%83%CE%B7%CF%82_%CF%84%CE%B9%CE%BC%CE%AE%CF%82" title="Θεώρημα μέσης τιμής – grščina" lang="el" hreflang="el" data-title="Θεώρημα μέσης τιμής" data-language-autonym="Ελληνικά" data-language-local-name="grščina" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mean_value_theorem" title="Mean value theorem – angleščina" lang="en" hreflang="en" data-title="Mean value theorem" data-language-autonym="English" data-language-local-name="angleščina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Meznombra_valora_teoremo" title="Meznombra valora teoremo – esperanto" lang="eo" hreflang="eo" data-title="Meznombra valora teoremo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teorema_del_valor_medio" title="Teorema del valor medio – španščina" lang="es" hreflang="es" data-title="Teorema del valor medio" data-language-autonym="Español" data-language-local-name="španščina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Lagrange%27i_keskv%C3%A4%C3%A4rtusteoreem" title="Lagrange'i keskväärtusteoreem – estonščina" lang="et" hreflang="et" data-title="Lagrange'i keskväärtusteoreem" data-language-autonym="Eesti" data-language-local-name="estonščina" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Batez_besteko_balioaren_teorema" title="Batez besteko balioaren teorema – baskovščina" lang="eu" hreflang="eu" data-title="Batez besteko balioaren teorema" data-language-autonym="Euskara" data-language-local-name="baskovščina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%82%D8%B6%DB%8C%D9%87_%D9%85%D9%82%D8%AF%D8%A7%D8%B1_%D9%85%DB%8C%D8%A7%D9%86%DA%AF%DB%8C%D9%86" title="قضیه مقدار میانگین – perzijščina" lang="fa" hreflang="fa" data-title="قضیه مقدار میانگین" data-language-autonym="فارسی" data-language-local-name="perzijščina" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Differentiaalilaskennan_v%C3%A4liarvolause" title="Differentiaalilaskennan väliarvolause – finščina" lang="fi" hreflang="fi" data-title="Differentiaalilaskennan väliarvolause" data-language-autonym="Suomi" data-language-local-name="finščina" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_des_accroissements_finis" title="Théorème des accroissements finis – francoščina" lang="fr" hreflang="fr" data-title="Théorème des accroissements finis" data-language-autonym="Français" data-language-local-name="francoščina" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Teorema_do_valor_medio" title="Teorema do valor medio – galicijščina" lang="gl" hreflang="gl" data-title="Teorema do valor medio" data-language-autonym="Galego" data-language-local-name="galicijščina" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%A2%D7%A8%D7%9A_%D7%94%D7%9E%D7%9E%D7%95%D7%A6%D7%A2_%D7%A9%D7%9C_%D7%9C%D7%92%D7%A8%D7%90%D7%A0%D7%96%27" title="משפט הערך הממוצע של לגראנז' – hebrejščina" lang="he" hreflang="he" data-title="משפט הערך הממוצע של לגראנז'" data-language-autonym="עברית" data-language-local-name="hebrejščina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AE%E0%A4%BE%E0%A4%A7%E0%A5%8D%E0%A4%AF%E0%A4%AE%E0%A4%BE%E0%A4%A8_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%87%E0%A4%AF" title="माध्यमान प्रमेय – hindijščina" lang="hi" hreflang="hi" data-title="माध्यमान प्रमेय" data-language-autonym="हिन्दी" data-language-local-name="hindijščina" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Riemannov_teorem" title="Riemannov teorem – hrvaščina" lang="hr" hreflang="hr" data-title="Riemannov teorem" data-language-autonym="Hrvatski" data-language-local-name="hrvaščina" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Lagrange-f%C3%A9le_k%C3%B6z%C3%A9p%C3%A9rt%C3%A9kt%C3%A9tel" title="Lagrange-féle középértéktétel – madžarščina" lang="hu" hreflang="hu" data-title="Lagrange-féle középértéktétel" data-language-autonym="Magyar" data-language-local-name="madžarščina" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teorema_nilai_purata" title="Teorema nilai purata – indonezijščina" lang="id" hreflang="id" data-title="Teorema nilai purata" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijščina" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Me%C3%B0algildissetningin" title="Meðalgildissetningin – islandščina" lang="is" hreflang="is" data-title="Meðalgildissetningin" data-language-autonym="Íslenska" data-language-local-name="islandščina" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teorema_di_Lagrange" title="Teorema di Lagrange – italijanščina" lang="it" hreflang="it" data-title="Teorema di Lagrange" data-language-autonym="Italiano" data-language-local-name="italijanščina" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%B9%B3%E5%9D%87%E5%80%A4%E3%81%AE%E5%AE%9A%E7%90%86" title="平均値の定理 – japonščina" lang="ja" hreflang="ja" data-title="平均値の定理" data-language-autonym="日本語" data-language-local-name="japonščina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8F%89%EA%B7%A0%EA%B0%92_%EC%A0%95%EB%A6%AC" title="평균값 정리 – korejščina" lang="ko" hreflang="ko" data-title="평균값 정리" data-language-autonym="한국어" data-language-local-name="korejščina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Teorema_de_Lagrange" title="Teorema de Lagrange – Lombard" lang="lmo" hreflang="lmo" data-title="Teorema de Lagrange" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Lagran%C5%BEo_vidutin%C4%97s_reik%C5%A1m%C4%97s_teorema" title="Lagranžo vidutinės reikšmės teorema – litovščina" lang="lt" hreflang="lt" data-title="Lagranžo vidutinės reikšmės teorema" data-language-autonym="Lietuvių" data-language-local-name="litovščina" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Lagran%C5%BEa_teor%C4%93ma" title="Lagranža teorēma – latvijščina" lang="lv" hreflang="lv" data-title="Lagranža teorēma" data-language-autonym="Latviešu" data-language-local-name="latvijščina" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B8_%D0%B7%D0%B0_%D1%81%D1%80%D0%B5%D0%B4%D0%BD%D0%B0_%D0%B2%D1%80%D0%B5%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Теореми за средна вредност – makedonščina" lang="mk" hreflang="mk" data-title="Теореми за средна вредност" data-language-autonym="Македонски" data-language-local-name="makedonščina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Middelwaardestelling" title="Middelwaardestelling – nizozemščina" lang="nl" hreflang="nl" data-title="Middelwaardestelling" data-language-autonym="Nederlands" data-language-local-name="nizozemščina" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Middelverdisetningen" title="Middelverdisetningen – knjižna norveščina" lang="nb" hreflang="nb" data-title="Middelverdisetningen" data-language-autonym="Norsk bokmål" data-language-local-name="knjižna norveščina" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Twierdzenie_Lagrange%E2%80%99a_(rachunek_r%C3%B3%C5%BCniczkowy)" title="Twierdzenie Lagrange’a (rachunek różniczkowy) – poljščina" lang="pl" hreflang="pl" data-title="Twierdzenie Lagrange’a (rachunek różniczkowy)" data-language-autonym="Polski" data-language-local-name="poljščina" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Teorema_%C3%ABd_Cauchy_dle_ch%C3%ABrs%C3%B9e_fin%C3%ACe" title="Teorema ëd Cauchy dle chërsùe finìe – Piedmontese" lang="pms" hreflang="pms" data-title="Teorema ëd Cauchy dle chërsùe finìe" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teorema_do_valor_m%C3%A9dio" title="Teorema do valor médio – portugalščina" lang="pt" hreflang="pt" data-title="Teorema do valor médio" data-language-autonym="Português" data-language-local-name="portugalščina" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teorema_cre%C8%99terilor_finite" title="Teorema creșterilor finite – romunščina" lang="ro" hreflang="ro" data-title="Teorema creșterilor finite" data-language-autonym="Română" data-language-local-name="romunščina" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0_%D0%BA%D0%BE%D0%BD%D0%B5%D1%87%D0%BD%D1%8B%D1%85_%D0%BF%D1%80%D0%B8%D1%80%D0%B0%D1%89%D0%B5%D0%BD%D0%B8%D0%B9" title="Формула конечных приращений – ruščina" lang="ru" hreflang="ru" data-title="Формула конечных приращений" data-language-autonym="Русский" data-language-local-name="ruščina" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Lagrangeova_veta_o_strednej_hodnote" title="Lagrangeova veta o strednej hodnote – slovaščina" lang="sk" hreflang="sk" data-title="Lagrangeova veta o strednej hodnote" data-language-autonym="Slovenčina" data-language-local-name="slovaščina" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Teorema_e_vler%C3%ABs_mesatare" title="Teorema e vlerës mesatare – albanščina" lang="sq" hreflang="sq" data-title="Teorema e vlerës mesatare" data-language-autonym="Shqip" data-language-local-name="albanščina" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B3%D1%80%D0%B0%D0%BD%D0%B6%D0%BE%D0%B2%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0" title="Лагранжова теорема – srbščina" lang="sr" hreflang="sr" data-title="Лагранжова 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class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B9%88%E0%B8%B2%E0%B8%A1%E0%B8%B1%E0%B8%8A%E0%B8%8C%E0%B8%B4%E0%B8%A1" title="ทฤษฎีบทค่ามัชฌิม – tajščina" lang="th" hreflang="th" data-title="ทฤษฎีบทค่ามัชฌิม" data-language-autonym="ไทย" data-language-local-name="tajščina" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Ortalama_de%C4%9Fer_teoremi" title="Ortalama değer teoremi – turščina" lang="tr" hreflang="tr" data-title="Ortalama değer teoremi" data-language-autonym="Türkçe" data-language-local-name="turščina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%BF%D1%80%D0%BE_%D1%81%D0%B5%D1%80%D0%B5%D0%B4%D0%BD%D1%94_%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%BD%D1%8F" title="Теорема про середнє значення – ukrajinščina" lang="uk" hreflang="uk" data-title="Теорема про середнє значення" data-language-autonym="Українська" data-language-local-name="ukrajinščina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%82%D8%B6%DB%8C%DB%81_%D9%82%D8%AF%D8%B1_%D9%88%D8%B3%D8%B7%DB%8C" title="قضیہ قدر وسطی – urdujščina" lang="ur" hreflang="ur" data-title="قضیہ قدر وسطی" data-language-autonym="اردو" data-language-local-name="urdujščina" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Lagranj_formulasi" title="Lagranj formulasi – uzbeščina" lang="uz" 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data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Videz</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Iz Wikipedije, proste enciklopedije</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sl" dir="ltr"><figure typeof="mw:File/Frame"><a href="/wiki/Slika:Mvt2_sl.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Mvt2_sl.svg/337px-Mvt2_sl.svg.png" decoding="async" width="337" height="248" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Mvt2_sl.svg/506px-Mvt2_sl.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Mvt2_sl.svg/674px-Mvt2_sl.svg.png 2x" data-file-width="337" data-file-height="248" /></a><figcaption>Za vsako funkcijo, ki je zvezna na [<i>a</i>, <i>b</i>] in odvedljiva na (<i>a</i>, <i>b</i>), obstaja neka točka <i>c</i> na odprtem intervalu (<i>a</i>, <i>b</i>), da je <i>sekanta</i>, ki povezuje obe končni točki intervala [<i>a</i>, <i>b</i>], vzporedna <i>tangenti</i> v <i>c</i>.</figcaption></figure> <p><b>Izrèk o povpréčni vrédnosti</b> (tudi <b>Lagrangeev izrèk</b> ali <b>izrèk o kônčnem prirástku fúnkcije</b>) je v <a href="/wiki/Matemati%C4%8Dna_analiza" title="Matematična analiza">matematični analizi</a> <a href="/wiki/Izrek" title="Izrek">izrek</a>, ki pravi, da v danem odseku gladke krivulje obstaja <a href="/wiki/To%C4%8Dka_(geometrija)" title="Točka (geometrija)">točka</a>, v kateri je <a href="/wiki/Odvod" title="Odvod">odvod</a> (nagib) krivulje enak »povprečnemu« odvodu intervala. Izrek se uporablja pri <a href="/wiki/Matemati%C4%8Dni_dokaz" title="Matematični dokaz">dokazovanju</a> izrekov, ki obravnavajo funkcije na intervalu. </p><p>Povprečna vrednost integrabilne funkcije na intervalu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [a,b]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [a,b]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.555ex; height:2.843ex;" alt="{\displaystyle [a,b]}"></span> je število: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {1}{b-a}}\int _{a}^{b}f(x)\,dx.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>b</mi> <mo>−</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {1}{b-a}}\int _{a}^{b}f(x)\,dx.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d9be0369b06a2a56b9ff5e4228847cc81d19dac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.921ex; height:6.343ex;" alt="{\displaystyle P={\frac {1}{b-a}}\int _{a}^{b}f(x)\,dx.}"></span> </p><p>Izrek lahko razumemo tudi s pomočjo <a href="/wiki/Gibanje" title="Gibanje">gibanja</a>. Če avtomobil prepotuje v eni uri 100 km in je njegova <i>povprečna</i> hitrost enaka 100 km/h, potem je morala biti v nekem trenutku njegova <i>trenutna</i> hitrost enaka natanko 100 km/h. </p><p>Izrek je prvi razvil <a href="/wiki/Joseph-Louis_de_Lagrange" title="Joseph-Louis de Lagrange">Joseph-Louis de Lagrange</a> in se imenuje tudi po njem. </p> <div class="mw-heading mw-heading2"><h2 id="Formalna_izjava">Formalna izjava</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Izrek_o_povpre%C4%8Dni_vrednosti&veaction=edit&section=1" title="Uredi razdelek: Formalna izjava" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Izrek_o_povpre%C4%8Dni_vrednosti&action=edit&section=1" title="Urejanje izvorne kode razdelka: Formalna izjava"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Naj je <a href="/wiki/Matemati%C4%8Dna_funkcija" class="mw-redirect" title="Matematična funkcija">funkcija</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2311a6a75c54b0ea085a381ba472c31d59321514" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.672ex; height:2.843ex;" alt="{\displaystyle y=f(x)}"></span> v zaprtem <a href="/wiki/Interval_(matematika)" title="Interval (matematika)">intervalu</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle [a,b]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [a,b]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.555ex; height:2.843ex;" alt="{\displaystyle [a,b]}"></span> <a href="/wiki/Zveznost" class="mw-redirect" title="Zveznost">zvezna</a> in v odprtem intervalu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (a,b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a,b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e5710198f33b00695903460983021e75860e2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.071ex; height:2.843ex;" alt="{\displaystyle (a,b)}"></span> <a href="/w/index.php?title=Odvedljivost&action=edit&redlink=1" class="new" title="Odvedljivost (stran ne obstaja)">odvedljiva</a>. Tedaj obstaja vsaj eno takšno <a href="/wiki/%C5%A0tevilo" title="Število">število</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \xi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ξ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \xi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.03ex; height:2.509ex;" alt="{\displaystyle \xi }"></span> med <i>a</i> in <i>b</i>, da je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {f(b)-f(a) \over b-a}=f'(\xi )\qquad a<\xi <b\;.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>b</mi> <mo>−</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>ξ</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mi>a</mi> <mo><</mo> <mi>ξ</mi> <mo><</mo> <mi>b</mi> <mspace width="thickmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {f(b)-f(a) \over b-a}=f'(\xi )\qquad a<\xi <b\;.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b14f5f6df27b487ac1f721cceb5a57a8dd626e6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:35.414ex; height:6.009ex;" alt="{\displaystyle {f(b)-f(a) \over b-a}=f'(\xi )\qquad a<\xi <b\;.}"></span></dd></dl> <p>Če pišemo drugače, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=a+h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=a+h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b6b083e53df04d709ae7dfa946f3937c1e624d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.505ex; height:2.343ex;" alt="{\displaystyle b=a+h}"></span> in označimo s <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vartheta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϑ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vartheta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d00eaf197c35bbfa391b9477490a4af955416837" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.374ex; height:2.176ex;" alt="{\displaystyle \vartheta }"></span> število med 0 in 1: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(a+h)=f(a)+hf'(a+\vartheta h)\qquad 0<\vartheta <1\;.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>h</mi> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>ϑ</mi> <mi>h</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mn>0</mn> <mo><</mo> <mi>ϑ</mi> <mo><</mo> <mn>1</mn> <mspace width="thickmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(a+h)=f(a)+hf'(a+\vartheta h)\qquad 0<\vartheta <1\;.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa4bae08a6914bdf830244d54733f97b1f78c790" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:46.523ex; height:3.009ex;" alt="{\displaystyle f(a+h)=f(a)+hf'(a+\vartheta h)\qquad 0<\vartheta <1\;.}"></span></dd></dl> <p>Posplošitev Lagrangeevega izreka je <a href="/w/index.php?title=Taylorjev_izrek&action=edit&redlink=1" class="new" title="Taylorjev izrek (stran ne obstaja)">Taylorjev izrek</a>. </p> <style data-mw-deduplicate="TemplateStyles:r5570670">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox table{background:transparent}.mw-parser-output .asbox p{margin:0}.mw-parser-output .asbox p+p{margin-top:0.25em}.mw-parser-output .asbox-body{font-style:italic}.mw-parser-output .asbox-note{font-size:smaller}.mw-parser-output .asbox .navbar{position:absolute;top:-0.75em;right:1em;display:none}</style><div role="note" class="metadata plainlinks asbox stub"><table role="presentation"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/Slika:E-to-the-i-pi.svg" class="mw-file-description"><img alt="Stub icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/34px-E-to-the-i-pi.svg.png" decoding="async" width="34" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/51px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td><td><p class="asbox-body">Ta matematični članek je <a href="/wiki/Wikipedija:%C5%A0krbina" title="Wikipedija:Škrbina">škrbina</a>. 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