{"id":661,"date":"2020-11-12T20:54:08","date_gmt":"2020-11-12T18:54:08","guid":{"rendered":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=661"},"modified":"2020-11-12T20:54:08","modified_gmt":"2020-11-12T18:54:08","slug":"parametros-conociendo-tangente-en-la-inflexion","status":"publish","type":"post","link":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=661","title":{"rendered":"Par\u00e1metros conociendo tangente en la inflexi\u00f3n"},"content":{"rendered":"<style type=\"text\/css\">\nboton {\n border: none;\n background: rgba(0,0,0,0);\n color: #3a7999;\n box-shadow: inset 0 0 0 3px #3a7999;\n padding: 10px;\n font-size: 125%;\n border-radius: 5px;\n position: relative;\n box-sizing: border-box;\n}\n<\/style>\n<p><script type=\"text\/javascript\">function SINO(cual) {\n   var elElemento=document.getElementById(cual);\n   if(elElemento.style.display == 'block') {\n      elElemento.style.display = 'none';\n   } else {\n      elElemento.style.display = 'block';\n   }\n}\n<\/script><\/p>\n<p>Terminamos hoy nuestra breve serie de c\u00e1lculo de par\u00e1metros, con una funci\u00f3n en la que se conoce la abscisa del punto de inflexi\u00f3n y la recta tangente en \u00e9l. Por supuesto, es muy semejante en planteamiento y ejecuci\u00f3n a los otros ya vistos.<\/p>\n<\/p>\n<p>Aqu\u00ed el enunciado del problema del d\u00eda:<\/p>\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\nConsideremos la funci\u00f3n \\(f:\\left(0\\,,+\\infty\\right)\\rightarrow\\mathbb{R}\\) definida mediante<br \/>\n\\[f\\left(x\\right)=a x^2 + b x + c + 2 \\ln\\left(x\\right)\\]<br \/>\nHallemos \\(a\\) , \\(b\\) y \\(c\\) sabiendo que para \\(x=1\\) presenta un punto de inflexi\u00f3n en el que la recta tangente tiene de ecuaci\u00f3n \\(y=2x+6\\)<br \/>\n<\/fieldset>\n<p>Si tienes dificultades o no sabes c\u00f3mo resolverlo, te recomiendo trabajarlo con el siguiente v\u00eddeo, donde est\u00e1 detalladamente resuelto:<\/p>\n<div style=\"text-align: center;\"><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/wlJ1PhlLVSI\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/div>\n<p>Una preguntita para ver si lo hemos asimilado:<\/p>\n<form name=\"ejercicio\">\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\n<div class=\"pregunta\">\n<div style=\"text-align: center;\">CUESTI\u00d3N<\/div>\n<p>Si la recta tangente a la gr\u00e1fica de la funci\u00f3n derivable \\(f\\) para \\(x=2\\) es \\(y=3x-1\\), entonces:<\/p>\n<table width=\"100%\" cellpadding=\"4\" cellspacing=\"0\">\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#10060; Incorrecto '\" type=\"radio\" \/> \\(f\\left(2\\right)=3 \\text{ y }f&#8217;\\left(2\\right)=0 \\).<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"10%\" style=\"border: none;\">\n<p align=\"center\"><boton><a href=\"javascript:void(0);\" onclick=\"SINO('suger1')\" style=\"text-decoration: none;\" title=\"Ver sugerencia\">&#10067;<\/a><\/boton><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#10060; Incorrecto '\" type=\"radio\" \/> \\(f\\left(x\\right)=3x-1\\)<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#9989; Correcto '\" type=\"radio\" \/> \\(f\\left(2\\right)=5 \\text{ y }f&#8217;\\left(2\\right)=3 \\).<\/p>\n<\/td>\n<td rowspan=\"2\" width=\"10%\" style=\"border: none;\">\n<p align=\"center\"><boton><a href=\"javascript:void(0);\" onclick=\"SINO('solu1')\" style=\"text-decoration: none;\" title=\"Ver soluci\u00f3n\"> &#9997; <\/a><\/boton><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td width=\"90%\" style=\"border: none;\">\n<p align=\"left\"><input name=\"p1\" onclick=\"document.ejercicio.feedback1.value=' &#10060; Incorrecto '\" type=\"radio\" \/> \\(f\\left(2\\right)=-1 \\text{ y }f&#8217;\\left(2\\right)=3 \\)<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<div style=\"text-align: center;\"><input name=\"feedback1\" size=\"10\" \/><\/div>\n<p>\n<\/div>\n<div id=\"suger1\" style=\"display: none;\">\n<hr \/>\n<p>Sugerencia:<\/p>\n<p>Recordemos que en el punto de tangencia la derivada es igual a la pendiente.<\/p>\n<p>Y debemos obtener la misma ordenada al sustituir la abscisa del punto de contacto en la funci\u00f3n y en la tangente.<\/p>\n<\/div>\n<div id=\"solu1\" style=\"display: none;\">\n<hr \/>\n<p>Soluci\u00f3n:<\/p>\n<p>Ya lo hemos visto muchas veces:<br \/>\n\\[f&#8217;\\left(2\\right)=m \\rightarrow f&#8217;\\left(2\\right)=3\\]<br \/>\nFunci\u00f3n y tangente coinciden para \\(x=2\\):<br \/>\n\\[f(2)=y(2) \\xrightarrow{3\\cdot2-1} f\\left(2\\right)=5\\]\n<\/p><\/div>\n<\/fieldset>\n<p>\n<\/form>\n<p>\u00bfTodo clarito? Eso espero, as\u00ed como se haya disfrutado con la pr\u00e1ctica.<\/p>\n<p>Gracias por la visita. Saludos<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Terminamos hoy nuestra breve serie de c\u00e1lculo de par\u00e1metros, con una funci\u00f3n en la que se conoce la abscisa del punto de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"post-templates\/post_nosidebar.php","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[59,58,50],"class_list":["post-661","post","type-post","status-publish","format-standard","hentry","category-matematicas-ii","tag-aplicaciones-de-las-derivadas","tag-calculo-diferencial","tag-video"],"_links":{"self":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/661","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=661"}],"version-history":[{"count":2,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/661\/revisions"}],"predecessor-version":[{"id":663,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/661\/revisions\/663"}],"wp:attachment":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}