{"id":1080,"date":"2021-12-17T16:32:51","date_gmt":"2021-12-17T11:02:51","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1080"},"modified":"2025-07-31T17:46:56","modified_gmt":"2025-07-31T12:16:56","slug":"study-materials-ncert-solutions-class-12-maths-chapter-6-applications-of-derivative","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative\/#NCERT_Solutions_for_Class_12_Maths_Chapter_6_Application_of_Derivatives\" title=\"NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives\">NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative\/#NCERT_Solutions_For_Class_12_Maths_Chapter_6_Exercises\" title=\"NCERT Solutions For Class 12 Maths Chapter 6 Exercises:\">NCERT Solutions For Class 12 Maths Chapter 6 Exercises:<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative\/#Key_Features_of_NCERT_Solutions_for_Class_12_Maths_Chapter_6_Application_of_Derivatives\" title=\"Key Features of NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives\">Key Features of NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative\/#Frequently_Asked_Questions_on_NCERT_Solutions_for_Class_12_Maths_Chapter_6\" title=\"Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 6\">Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 6<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative\/#What_are_the_main_applications_of_derivatives_in_our_daily_life_according_to_NCERT_Solutions_for_Class_12_Maths_Chapter_6\" title=\"What are the main applications of derivatives in our daily life according to NCERT Solutions for Class 12 Maths Chapter 6?\">What are the main applications of derivatives in our daily life according to NCERT Solutions for Class 12 Maths Chapter 6?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"auto\">Subject specialists have created NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives, which includes thorough solutions for reference. All of the questions from the textbook&#8217;s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Solutions for Class 12 provide useful solutions for improving conceptual knowledge.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in exams but also in helping Class 12 pupils perform well in upcoming competitive exams.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management is essential for getting the best results when answering questions.<\/span><\/p>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Chapter-6.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Chapter-6.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Chapter 6<br\/><\/a>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_6_Application_of_Derivatives\"><\/span><span style=\"font-size: 14pt;\">NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"none\">The rate of change of values, increasing and decreasing functions, tangents and normals, approximations, maxima and minima, and many other subjects are covered in this chapter of NCERT Solutions for Class 12 Maths. The following are some key concepts:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ol>\n<li><span data-contrast=\"none\"> A function f is said to be<\/span><\/li>\n<\/ol>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span data-contrast=\"none\">increasing on an interval (a, b) if x1 &lt; x2<\/span><span data-contrast=\"none\"> in (a, b) \u21d2 f(x<\/span><span data-contrast=\"none\">1) &lt; f(x2) for all x1, x2<\/span><span data-contrast=\"none\"> \u2208 (a, b)<\/span><\/li>\n<li><span data-contrast=\"none\">decreasing on (a,b) if x1 &lt; x 2<\/span><span data-contrast=\"none\"> in (a, b) \u21d2 f(x<\/span><span data-contrast=\"none\">1 ) &gt; f(x2 ) for all x1 , x2<\/span><span data-contrast=\"none\"> \u2208 (a, b).<\/span><\/li>\n<li><span data-contrast=\"none\">constant in (a, b), if f (x) = c for all x \u2208 (a, b), where c is a constant.<\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<ol start=\"2\">\n<li><span data-contrast=\"none\"> First Derivative Test<\/span><\/li>\n<li><span data-contrast=\"none\"> Second Derivative Test<\/span><\/li>\n<\/ol>\n<p><span data-contrast=\"none\">The NCERT Solutions for Class 12 Maths Chapter 6 can be a quick reference to help students understand crucial and complicated topics.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<h2 aria-level=\"3\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_For_Class_12_Maths_Chapter_6_Exercises\"><\/span><span style=\"font-size: 14pt;\"><b>NCERT Solutions For Class 12 Maths Chapter 6 Exercises:<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<table data-tablestyle=\"MsoNormalTable\" data-tablelook=\"1184\" aria-rowcount=\"7\">\n<tbody>\n<tr aria-rowindex=\"1\">\n<td data-celllook=\"69905\"><b><span data-contrast=\"auto\">Maths Class 12 NCERT Solutions Chapter 6 Exercises<\/span><\/b><\/td>\n<\/tr>\n<tr aria-rowindex=\"2\">\n<td data-celllook=\"69905\"><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative-exercise-6-1\" target=\"_blank\" rel=\"noopener\"><span data-contrast=\"auto\">Exercise 6.1 Class 12 Maths<\/span><\/a><\/td>\n<\/tr>\n<tr aria-rowindex=\"3\">\n<td data-celllook=\"69905\">Exercise 6.2 Class 12 Maths<\/a><\/td>\n<\/tr>\n<tr aria-rowindex=\"4\">\n<td data-celllook=\"69905\"><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative-exercise-6-3\" target=\"_blank\" rel=\"noopener\">Exercise 6.3 Class 12 Maths<\/a><\/td>\n<\/tr>\n<tr aria-rowindex=\"5\">\n<td data-celllook=\"69905\"><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative-exercise-6-4\" target=\"_blank\" rel=\"noopener\">Exercise 6.4 Class 12 Maths<\/a><\/td>\n<\/tr>\n<tr aria-rowindex=\"6\">\n<td data-celllook=\"69905\">Exercise 6.5 Class 12 Maths<\/td>\n<\/tr>\n<tr aria-rowindex=\"7\">\n<td data-celllook=\"69905\">Miscellaneous Exercise on Chapter 6 Class 12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 aria-level=\"3\"><span class=\"ez-toc-section\" id=\"Key_Features_of_NCERT_Solutions_for_Class_12_Maths_Chapter_6_Application_of_Derivatives\"><\/span><span style=\"font-size: 12pt;\">Key Features of NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li><span data-contrast=\"none\">NCERT Solutions will aid in the development of student confidence.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">The content is well-structured to make learning and understanding easier for students.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">The NCERT Solutions are based on the most recent CBSE curriculum update for 2021-22.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">This chapter will assist students in strengthening their understanding of derivatives.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">Students can use NCERT Solutions to help them with their assignments and competitive exams.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559739&quot;:160,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ol>\n<h4 aria-level=\"2\"><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions_on_NCERT_Solutions_for_Class_12_Maths_Chapter_6\"><\/span><span style=\"font-size: 12pt;\">Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 6<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p aria-level=\"3\"><span style=\"color: #0000ff;\"><strong>Why should I download Infinity learn NCERT Solutions for Class 12 Maths Chapter 6?<\/strong><\/span><\/p>\n<p><span data-contrast=\"auto\"><span style=\"color: #ff0000;\"><strong>Answer:<\/strong><\/span> There are various reasons why you should download Infinity Learn&#8217;s NCERT Solutions for Class 12 Maths Chapter 6 created by specialists.<\/span><\/p>\n<ol>\n<li><span data-contrast=\"auto\"> The CBSE board advises students to use the NCERT textbooks because they are one of the greatest study materials for exams.<\/span><\/li>\n<li><span data-contrast=\"auto\"> NCERT Solutions are important since they provide answers to all of the questions in the NCERT textbook in one spot.<\/span><\/li>\n<li><span data-contrast=\"auto\"> Infinity Learn&#8217;s subject matter specialists and teachers deliver solutions to assist students in performing well on term-wise exams.<\/span><\/li>\n<\/ol>\n\t<section class=\"sc_fs_faq sc_card \">\n\t\t<div>\n\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_are_the_main_applications_of_derivatives_in_our_daily_life_according_to_NCERT_Solutions_for_Class_12_Maths_Chapter_6\"><\/span>What are the main applications of derivatives in our daily life according to NCERT Solutions for Class 12 Maths Chapter 6?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t<div>\n\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t Derivatives are used to calculate the rate of change, growing or decreasing intervals, Lagrange&#8217;s Mean Value Theorem, Rolle&#8217;s Theorem, the point at which a tangent is parallel or perpendicular, the slope of a tangent or normal, and the approximate value of numbers, among other things. Our professionals explain these applications in simple and straightforward terms to help students grasp the key principles. Several examples are presented beneath each application to help students develop their conceptual understanding, regardless of their cognitive quotient. \t\t\t\t<\/p>\n\t\t\t<\/div>\n\t\t<\/div>\n\t<\/section>\n\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the main applications of derivatives in our daily life according to NCERT Solutions for Class 12 Maths Chapter 6?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Derivatives are used to calculate the rate of change, growing or decreasing intervals, Lagrange&#8217;s Mean Value Theorem, Rolle&#8217;s Theorem, the point at which a tangent is parallel or perpendicular, the slope of a tangent or normal, and the approximate value of numbers, among other things. Our professionals explain these applications in simple and straightforward terms to help students grasp the key principles. Several examples are presented beneath each application to help students develop their conceptual understanding, regardless of their cognitive quotient.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives, which includes thorough solutions for [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Class 12 Maths Chapter 6 Application of Derivatives","_yoast_wpseo_title":"NCERT Solutions Class 12 Maths Chapter 6 Application of Derivatives","_yoast_wpseo_metadesc":"NCERT Solutions for Class 12 Maths Chapter 6 - Application of Derivatives solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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