{"id":590,"date":"2020-10-20T13:07:21","date_gmt":"2020-10-20T11:07:21","guid":{"rendered":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=590"},"modified":"2020-10-20T13:07:21","modified_gmt":"2020-10-20T11:07:21","slug":"tangente-paralela-a-una-recta-dada","status":"publish","type":"post","link":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=590","title":{"rendered":"Tangente paralela a una recta dada"},"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>En la entrada de hoy vamos a examinar un t\u00edpico problema de recta tangente, dentro del \u00e1mbito de las derivadas: dadas una curva y una recta, \u00bfhay alguna tangente a la curva paralela a la recta dada? En caso afirmativo: \u00bfen qu\u00e9 punto hay que trazarla?<\/p>\n<p>Vamos a estudiarlo anal\u00edtivamente:<\/p>\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\nCalculemos la ecuaci\u00f3n de la recta tangente a la gr\u00e1fica de la funci\u00f3n<br \/>\n\\[ f\\left(x\\right) = x^2-2x\\]<br \/>\nque es paralela a la recta que pasa por los puntos<br \/>\n\\[ A\\left(1\\,,-1\\right) \\quad \\text{y}\\quad B\\left(3\\,,3\\right)\\]<\/fieldset>\n<p>En el siguiente v\u00eddeo lo podemos ver resuelto detenidamente:<\/p>\n<div style=\"text-align: center;\">\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/NprKAFCHGSc\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<\/div>\n<p>Para ver si lo has captado, intenta responder a esta<\/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>Cuando derivamos una funci\u00f3n polin\u00f3mica a trozos, en un separa-f\u00f3rmulas:<\/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\" \/> La ecuaci\u00f3n de la tangente es la derivada: \\(y= 2x-2\\).<\/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\" \/> No existe porque la curva es una par\u00e1bola.<\/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\" \/> Hemos de igualar la derivada a la ecuaci\u00f3n de la recta dada.<\/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=' &#9989; Correcto '\" type=\"radio\" \/> Hemos de igualar la derivada a la pendiente de \\(AB\\).<\/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>La pendiente de la tangente es la derivada en el punto de tangencia.<\/p>\n<\/div>\n<div id=\"solu1\" style=\"display: none;\">\n<hr \/>\n<p>Soluci\u00f3n:<\/p>\n<p>La tangente y la recta dada han de tener la misma pendiente si son paralelas y la pendiente de la tangente es igual a la derivada: hemos de igualar la derivada a la pendiente de la recta dada.<\/p>\n<\/div>\n<\/fieldset>\n<p>\n<\/form>\n<p>Como vemos, el C\u00e1lculo Diferencial da respuesta a cl\u00e1sicos problemas de \u00edndole geom\u00e9trico. Espero que se haya comprendido y que os haya gustado.<\/p>\n<p>Gracias por la visita. \u00a1Hasta otra!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>En la entrada de hoy vamos a examinar un t\u00edpico problema de recta tangente, dentro del \u00e1mbito de las derivadas: dadas una [&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":[57,58,50],"class_list":["post-590","post","type-post","status-publish","format-standard","hentry","category-matematicas-ii","tag-ampliacion-de-derivadas","tag-calculo-diferencial","tag-video"],"_links":{"self":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/590","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=590"}],"version-history":[{"count":3,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/590\/revisions"}],"predecessor-version":[{"id":593,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/590\/revisions\/593"}],"wp:attachment":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=590"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=590"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=590"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}