{"id":5058,"date":"2015-11-20T11:09:50","date_gmt":"2015-11-20T10:09:50","guid":{"rendered":"http:\/\/www.matematicaok.it\/?p=5058"},"modified":"2015-11-20T11:15:29","modified_gmt":"2015-11-20T10:15:29","slug":"teorema-di-rolle","status":"publish","type":"post","link":"https:\/\/www.matematicaok.com\/?p=5058","title":{"rendered":"Teorema di Rolle"},"content":{"rendered":"<p>Sia\u00a0y=f(x) una <strong>funzione continua<\/strong>\u00a0in un intervallo chiuso e limitato\u00a0<strong>[a,b]\u00a0<\/strong>e <strong>derivabile<\/strong> nei punti interni di tale\u00a0intervallo <strong>(a,b)<\/strong>; \u00a0se <strong>\u00a0f(a) = f(b)<\/strong>, allora esiste almeno un punto c\u00a0di (a,b)\u00a0tale che <strong>f &#8216;(c)=0<\/strong><\/p>\n<p><a href=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/SignGeoRolle.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-5061\" src=\"http:\/\/www.matematicaok.it\/wp-content\/uploads\/2015\/11\/SignGeoRolle-1024x468.png\" alt=\"Teorema di Rolle\" width=\"677\" height=\"309\" srcset=\"https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/SignGeoRolle-1024x468.png 1024w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/SignGeoRolle-300x137.png 300w, https:\/\/www.matematicaok.com\/wp-content\/uploads\/2015\/11\/SignGeoRolle.png 1423w\" sizes=\"auto, (max-width: 677px) 100vw, 677px\" \/><\/a><\/p>\n<p><strong>OSSERVAZIONE:<\/strong><br \/>\n<span style=\"text-decoration: underline;\">Significato\u00a0geometrico del Teorema di Rolle<\/span>: \u00e8 evidente\u00a0che \u00a0se valgono le ipotesi del teorema, esiste almeno un punto interno all&#8217;intervallo\u00a0[a,b]\u00a0in\u00a0cui la tangente alla curva \u00e8 parallela all&#8217;asse delle x<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sia\u00a0y=f(x) una funzione continua\u00a0in un intervallo chiuso e limitato\u00a0[a,b]\u00a0e derivabile nei punti interni di tale\u00a0intervallo (a,b); \u00a0se \u00a0f(a) = f(b), allora esiste almeno un punto c\u00a0di (a,b)\u00a0tale che f &#8216;(c)=0 OSSERVAZIONE: Significato\u00a0geometrico del Teorema di Rolle: \u00e8 evidente\u00a0che \u00a0se valgono le ipotesi del teorema, esiste almeno un punto interno all&#8217;intervallo\u00a0[a,b]\u00a0in\u00a0cui la tangente alla curva \u00e8 parallela all&#8217;asse delle x<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[143,168,204],"tags":[],"class_list":["post-5058","post","type-post","status-publish","format-standard","hentry","category-analisi-matematica","category-derivabilita","category-teorema-di-rolle"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p85Wmq-1jA","_links":{"self":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5058","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5058"}],"version-history":[{"count":3,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5058\/revisions"}],"predecessor-version":[{"id":5062,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=\/wp\/v2\/posts\/5058\/revisions\/5062"}],"wp:attachment":[{"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5058"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5058"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matematicaok.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5058"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}