{"id":12506,"date":"2017-02-11T15:41:16","date_gmt":"2017-02-11T14:41:16","guid":{"rendered":"http:\/\/www.valcon.it\/pp\/?p=12506"},"modified":"2025-03-25T09:42:48","modified_gmt":"2025-03-25T08:42:48","slug":"es2003-5","status":"publish","type":"post","link":"https:\/\/www.valcon.it\/pp\/es2003-5\/","title":{"rendered":"Esame di Stato 2003 &#8211; 5"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.valcon.it\/pp\/seconda-prova-mat\/\">Esame<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.valcon.it\/pp\/calcolo-radici\/\">Radici e zeri<\/a><\/div>\n<\/div>\n\n\n\n\n\n<p>La funzione <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-b1929dff870be2ef9cf183172fed8ab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#94;&#51;&#32;&#45;&#32;&#51;&#32;&#120;&#94;&#50;&#32;&#43;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\"\/>&nbsp;ha un solo zero reale, vale a dire che il suo grafico interseca una sola volta l\u2019asse delle ascisse.<br>Fornire un\u2019esauriente dimostrazione di questo fatto e stabilire se lo zero della funzione \u00e8 positivo o negativo.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Esistenza<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-97d433ed086107410f9c629812d8ceed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#32;&#61;&#32;&#50;&#120;&#94;&#51;&#32;&#45;&#32;&#51;&#32;&#120;&#94;&#50;&#32;&#43;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"163\" style=\"vertical-align: -5px;\"\/>, continua in R<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-630949d5ff3a7eccb90b5105962a39ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#108;&#105;&#109;&#95;&#123;&#120;&#92;&#116;&#111;&#45;&#92;&#105;&#110;&#102;&#116;&#121;&#125;&#102;&#40;&#120;&#41;&#61;&#45;&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"138\" style=\"vertical-align: -12px;\"\/><\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-c5f988ba2b83f3cc511a0a89d03fca5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#108;&#105;&#109;&#95;&#123;&#120;&#92;&#116;&#111;&#32;&#43;&#92;&#105;&#110;&#102;&#116;&#121;&#125;&#102;&#40;&#120;&#41;&#61;&#43;&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"138\" style=\"vertical-align: -13px;\"\/><\/li>\n\n\n\n<li>Teorema degli zeri: esiste almeno uno zero in R.<br><em>Tutte le funzioni polinomiali di grado dispari hanno almeno uno zero reale.<\/em><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Unicit\u00e0<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-8c34cb2882175bd7c68436ac8de21f27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#32;&#61;&#32;&#54;&#120;&#94;&#50;&#45;&#54;&#120;&#32;&#61;&#32;&#54;&#120;&#40;&#120;&#45;&#49;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"226\" style=\"vertical-align: -5px;\"\/><\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-e01726bbf9927f0e64c977ae1a1416fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"\/>\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-da990ed3f462c5d95d44d3f74fa86c96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#49;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: -3px;\"\/><\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-5e3d83fdf57749786be77ccb257331e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#50;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: -3px;\"\/><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>x &lt; 0: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-e0e531379d5ad440b61a1b28ee4226b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#32;&#62;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"\/>, f(x) crescente<\/li>\n\n\n\n<li>0 &lt; x &lt; 1: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-41bcc34d83467591d2bfeb839107c637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#32;&#60;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"\/>, f(x) decrescente<\/li>\n\n\n\n<li>x &gt; 1: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-e0e531379d5ad440b61a1b28ee4226b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#39;&#40;&#120;&#41;&#32;&#62;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"\/>, f(x) crescente<\/li>\n\n\n\n<li>x=0, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-a75370ab3a1be2750dfeeb4218cb41ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#48;&#41;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/>, massimo relativo<\/li>\n\n\n\n<li>x=1, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-585b61e1c7da89bf1a5b44ef089b6267_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#49;&#41;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/>, minimo relativo<\/li>\n\n\n\n<li>x &gt; 0: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-7ed796487df80967ad6281a6aa7dfb38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#41;&#32;&#62;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"67\" style=\"vertical-align: -5px;\"\/><\/li>\n\n\n\n<li>x &lt; 0: f(x) crescente, un solo zero reale<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Valore<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-1f8122bd3ddc4659b718fb9bb541919e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#45;&#49;&#41;&#32;&#61;&#32;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -5px;\"\/><\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-9fd99b9df71e078e73164fe8a9156510_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#48;&#41;&#32;&#61;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"\/><\/li>\n\n\n\n<li>Teorema degli zeri: esiste <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-f2ec800eef56bc532c94239beee2e595_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#48;&#32;&#92;&#105;&#110;&#32;&#40;&#45;&#49;&#44;&#32;&#48;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"\/> tale che <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.valcon.it\/pp\/wp-content\/ql-cache\/quicklatex.com-3dbf3f4a224d2d12501e61a79de81bb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#40;&#120;&#95;&#48;&#41;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"\/><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusione<\/h2>\n\n\n\n<p>La funzione ha un solo zero reale ed \u00e8 negativo.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Approssimazione<\/h2>\n\n\n\n<p>&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>La funzione $2x^3 &#8211; 3 x^2 + 2$&nbsp;ha un solo zero reale, vale a dire che il suo grafico interseca una sola volta l\u2019asse delle ascisse.Fornire un\u2019esauriente dimostrazione di questo fatto e stabilire se lo zero della funzione \u00e8 positivo o negativo. Esistenza Unicit\u00e0 Valore Conclusione La funzione ha un solo zero reale ed \u00e8 &#8230; <a title=\"Esame di Stato 2003 &#8211; 5\" class=\"read-more\" href=\"https:\/\/www.valcon.it\/pp\/es2003-5\/\" aria-label=\"Per saperne di pi\u00f9 su Esame di Stato 2003 &#8211; 5\">Leggi tutto<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[116],"tags":[],"class_list":["post-12506","post","type-post","status-publish","format-standard","hentry","category-seconda-prova-mat"],"_links":{"self":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/12506","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/comments?post=12506"}],"version-history":[{"count":4,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/12506\/revisions"}],"predecessor-version":[{"id":54564,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/posts\/12506\/revisions\/54564"}],"wp:attachment":[{"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/media?parent=12506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/categories?post=12506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.valcon.it\/pp\/wp-json\/wp\/v2\/tags?post=12506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}