{"id":6633,"date":"2011-03-21T12:12:31","date_gmt":"2011-03-21T12:12:31","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6633"},"modified":"2021-12-26T17:12:44","modified_gmt":"2021-12-26T17:12:44","slug":"considere-a-funcao-quadratica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6633","title":{"rendered":"Considere a fun\u00e7\u00e3o quadr\u00e1tica"},"content":{"rendered":"<p><ul id='GTTabs_ul_6633' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6633' class='GTTabs_curr'><a  id=\"6633_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6633' ><a  id=\"6633_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6633'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considere a fun\u00e7\u00e3o quadr\u00e1tica definida por $g(x)=3{{x}^{2}}+6x+5$.<\/p>\n<ol>\n<li>Resolva a equa\u00e7\u00e3o $g'(x)=0$, determine as coordenadas do v\u00e9rtice da par\u00e1bola gr\u00e1fico de g e apresente um esbo\u00e7o desse gr\u00e1fico.<\/li>\n<li>Use o gr\u00e1fico constru\u00eddo em 1 para mostrar que a fun\u00e7\u00e3o polinomial $h:x\\to {{x}^{3}}+3{{x}^{2}}+5x+7$ n\u00e3o tem extremos e, em seguida, esboce o gr\u00e1fico de h.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6633' onClick='GTTabs_show(1,6633)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6633'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,\n<p>$\\begin{array}{*{35}{l}}<br \/>\ng'(x)=0 &amp; \\Leftrightarrow\u00a0 &amp; 6x+6=0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; x=-1\u00a0 \\\\<br \/>\n\\end{array}$<\/p>\n<table class=\"aligncenter\" style=\"width: 60%;\" border=\"1\" cellspacing=\"4\" cellpadding=\"4\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">$x$<\/td>\n<td style=\"text-align: left;\">$-\\infty $<\/td>\n<td style=\"text-align: center;\">$-1$<\/td>\n<td style=\"text-align: right;\">$+\\infty $<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$g'(x)$<\/td>\n<td style=\"text-align: center;\">&#8211;<\/td>\n<td style=\"text-align: center;\">$0$<\/td>\n<td style=\"text-align: center;\">+<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">$g(x)$<\/td>\n<td style=\"text-align: center;\">$\\searrow $<\/td>\n<td style=\"text-align: center;\">$2$<\/td>\n<td style=\"text-align: center;\">$\\nearrow $<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>O v\u00e9rtice da par\u00e1bola, gr\u00e1fico da fun\u00e7\u00e3o g, \u00e9 o ponto $V(-1,2)$.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6634\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6634\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001.png\" data-orig-size=\"690,468\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001.png\" class=\"aligncenter wp-image-6634\" title=\"G1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001.png\" alt=\"\" width=\"540\" height=\"366\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001.png 690w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001-300x203.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001-150x101.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra001-400x271.png 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/a><\/p>\n<\/li>\n<li>Ora, $h'(x)=g(x)=3{{x}^{2}}+6x+5$.\n<p>Como $g(x)&gt;0,\\forall x\\in \\mathbb{R}$, isto \u00e9, como $h'(x)&gt;0,\\forall x\\in \\mathbb{R}$, ent\u00e3o a fun\u00e7\u00e3o h n\u00e3o possui extremos relativos, visto ser estritamente crescente.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6635\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6635\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002.png\" data-orig-size=\"690,468\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002.png\" class=\"aligncenter wp-image-6635\" title=\"G2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002.png\" alt=\"\" width=\"540\" height=\"366\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002.png 690w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002-300x203.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002-150x101.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/21-03-2011-Ecra002-400x271.png 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/a><\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6633' onClick='GTTabs_show(0,6633)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considere a fun\u00e7\u00e3o quadr\u00e1tica definida por $g(x)=3{{x}^{2}}+6x+5$. Resolva a equa\u00e7\u00e3o $g'(x)=0$, determine as coordenadas do v\u00e9rtice da par\u00e1bola gr\u00e1fico de g e apresente um esbo\u00e7o desse gr\u00e1fico. Use o gr\u00e1fico constru\u00eddo&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19447,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,134],"tags":[145,144],"series":[],"class_list":["post-6633","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-derivadas","tag-derivadas-2","tag-extremos-relativos"],"views":2285,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/Funcao_11-p196-ex44.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6633"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6633\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19447"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6633"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6633"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}