{"id":1911,"date":"2021-12-23T12:33:27","date_gmt":"2021-12-23T07:03:27","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1911"},"modified":"2022-05-30T15:15:13","modified_gmt":"2022-05-30T09:45:13","slug":"study-materials-ncert-solutions-class-12-maths-chapter-6-applications-of-derivative-exercise-6-3","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative-exercise-6-3\/","title":{"rendered":"NCERT Solution of Exercise 6.3 Class 12 Maths Chapter 6"},"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-exercise-6-3\/#Chapter_6_Exercise_63_Class_12_Mathematics_Solutions\" title=\"Chapter 6 Exercise 6.3 Class 12 Mathematics Solutions\">Chapter 6 Exercise 6.3 Class 12 Mathematics Solutions<\/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-exercise-6-3\/#Chapter_6_Exercise_63_Class_12_Mathematics_Solved_Solutions_Benefits\" title=\"Chapter 6 Exercise 6.3 Class 12 Mathematics Solved Solutions Benefits\">Chapter 6 Exercise 6.3 Class 12 Mathematics Solved Solutions Benefits<\/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-exercise-6-3\/#The_following_are_some_of_the_advantages_of_employing_these_solutions\" title=\"The following are some of the advantages of employing these solutions:\">The following are some of the advantages of employing these solutions:<\/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-exercise-6-3\/#FAQs_Frequently_Asked_Questions\" title=\"FAQs (Frequently Asked Questions)\">FAQs (Frequently Asked Questions)<\/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-exercise-6-3\/#What_are_the_benefits_of_NCERT_solutions_for_kids_in_class_12\" title=\"What are the benefits of NCERT solutions for kids in class 12?\">What are the benefits of NCERT solutions for kids in class 12?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative-exercise-6-3\/#What_does_derivatives_application_entail\" title=\"What does derivatives application entail?\">What does derivatives application entail?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-6-applications-of-derivative-exercise-6-3\/#How_many_questions_are_in_the_NCERT_Solutions_for_Class_12_Maths_Chapter_6_Exercise_63\" title=\"How many questions are in the NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.3?\">How many questions are in the NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.3?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"auto\">For some pupils, math can be a difficult subject. Because of the increased strain, it is especially difficult for pupils studying for their 12th board exam. Most students seem to avoid the chapter Application of Derivatives since it is confusing and difficult to understand. This practice is presented so that students can better comprehend the chapter. Application of Derivatives is a crucial chapter for students who wish to pursue math in post-secondary education. Students may find the application of derivatives quite complicated and time-consuming, so they must be able to Learn the chapter understandably. The notes offered in this post are free and easily accessible at all times. Every sum in the NCERT book&#8217;s exercise 6.3 is answered and described here in the simplest way possible for students to grasp. Before beginning this chapter, students must understand the fundamental concepts of tangents and derivatives; failing to do so will make it difficult to solve the chapter&#8217;s sums.<\/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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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/1911\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: 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\/Exercise-6.3.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\/Exercise-6.3.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\">Exercise 6.3<br\/><\/a>\n<h2 aria-level=\"2\"><span class=\"ez-toc-section\" id=\"Chapter_6_Exercise_63_Class_12_Mathematics_Solutions\"><\/span><span style=\"font-size: 14pt;\"><span style=\"color: #0000ff;\">Chapter 6 Exercise 6.3 Class 12 Mathematics Solutions<\/span><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">Chapter 6 of <span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\" target=\"_blank\" rel=\"noopener\">class 12 mathematics<\/a><\/span> is divided into two sections: tangents and normals and an activity. Math is an important subject for kids to Learn because it is required for students who have chosen to study science or intend to pursue engineering. Pupils must comprehend 12th math because it serves as the foundation for any hard science disciplines or engineering courses they may pursue. Tangents and normals \u2013 students are given an overview of the tangent line and the normal line in chapter 6 exercise 6.3. Theoretical information is presented in this chapter, which is highly important for students to grasp since they will be able to answer complex problems if they understand all of the concepts and figures. Before moving further with the subject, students must grasp all theoretical principles. The equation of a straight line and the slope at any needed point are covered in this chapter. The slope and equation and the slope of the tangent to the curve and its process as a whole are all explained inside the theory. Because the normal is perpendicular to the tangent, the normal slope may be determined. This derivation is used to create the formulae.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Exercise &#8211; There are 27 questions in this chapter 6 exercise 6.3 for students to solve, all of which are centered on the principles of tangents and normals. The majority of the questions require students to calculate the slope value using the tangents of the corresponding equations. The y-axis equations, as well as their x-axis coordinates, are presented in the questions. The values of the slopes are calculated first in the sums, and then the coordinates are entered. This is the most efficient method for completing the calculations. Because each problem is distinct, students will find the step-by-step technique to solve each sum in these <span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\" target=\"_blank\" rel=\"noopener\">NCERT solutions<\/a><\/span>. It would help to decide where the tangent is parallel to the chord that connects the two points in some problems. However, this problem is significantly different and more difficult than the others in chapter 6, exercise 6.3; the solutions provided here show how to approach each step. As you move through the exercise, the problem becomes a little more hard because some require you to form the equation of varied slopes.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Slopes and tangents have been calculated in various ways in Infinity Learn, all of which have been taught in a way that students can grasp.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Chapter_6_Exercise_63_Class_12_Mathematics_Solved_Solutions_Benefits\"><\/span><span style=\"color: #0000ff; font-size: 14pt;\"><b>Chapter 6 Exercise 6.3 Class 12 Mathematics Solved Solutions Benefits<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">These solutions assist students in comprehending the numerous challenges underlying tangents and slopes and how simple they are to solve. Using these solutions has a number of advantages.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"The_following_are_some_of_the_advantages_of_employing_these_solutions\"><\/span><span style=\"color: #0000ff; font-size: 12pt;\"><b>The following are some of the advantages of employing these solutions:<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"auto\">The solutions show students how to solve each problem step by step, making it easier to understand.<\/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 data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><span data-contrast=\"auto\">Experts in the field solve the problems, and students can compare their responses to these solutions to see if they got the appropriate answers.<\/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 data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><span data-contrast=\"auto\">The most recent CBSE criteria handle these problems, so pupils don&#8217;t have to worry about whether or not what they&#8217;re doing is appropriate.<\/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 data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"4\" data-aria-level=\"1\"><span data-contrast=\"auto\">These solutions can be used as revision material during a last-minute study session.<\/span><\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"FAQs_Frequently_Asked_Questions\"><\/span><span style=\"color: #000000; font-size: 14pt;\"><b>FAQs (Frequently Asked Questions)<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_are_the_benefits_of_NCERT_solutions_for_kids_in_class_12\"><\/span>What are the benefits of NCERT solutions for kids in class 12?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tClass 12 is one of the most important chapters in a student's academic career. It serves as a bridge between high school and college, and grades indicate a student's academic performance. These NCERT solutions give pupils the greatest answers and the most up-to-date techniques for solving them by CBSE requirements. These solutions demonstrate how to solve sums, and students can use the same strategy used in the exam for their problems.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_does_derivatives_application_entail\"><\/span>What does derivatives application entail?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe use of derivatives allows students to solve problems involving slopes and tangents. The slopes' coordinates are provided in some circumstances, and an equation must be derived from them. Students must grasp the theoretical concepts presented in this chapter; only then will they be able to proceed with solving the sum. Tangents and normals are included in Chapter 6 exercise 6.3, as well as the exercise.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"How_many_questions_are_in_the_NCERT_Solutions_for_Class_12_Maths_Chapter_6_Exercise_63\"><\/span>How many questions are in the NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.3?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA total of 27 have been provided with solutions in the NCERT Solutions for Class 12 Maths Chapter 6 exercise 6.3 for the students' ease of comprehension. To ensure clear knowledge and thus good scores in the exam, you can get the NCERT Solutions for free from the Infinity Learn website or the Infinity Learn app. Because the solutions were generated by specialists, they are a trustworthy source and provide a well-rounded learning experience.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\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\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the benefits of NCERT solutions for kids in class 12?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Class 12 is one of the most important chapters in a student's academic career. It serves as a bridge between high school and college, and grades indicate a student's academic performance. These NCERT solutions give pupils the greatest answers and the most up-to-date techniques for solving them by CBSE requirements. These solutions demonstrate how to solve sums, and students can use the same strategy used in the exam for their problems.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What does derivatives application entail?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The use of derivatives allows students to solve problems involving slopes and tangents. The slopes' coordinates are provided in some circumstances, and an equation must be derived from them. Students must grasp the theoretical concepts presented in this chapter; only then will they be able to proceed with solving the sum. Tangents and normals are included in Chapter 6 exercise 6.3, as well as the exercise.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How many questions are in the NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.3?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A total of 27 have been provided with solutions in the NCERT Solutions for Class 12 Maths Chapter 6 exercise 6.3 for the students' ease of comprehension. To ensure clear knowledge and thus good scores in the exam, you can get the NCERT Solutions for free from the Infinity Learn website or the Infinity Learn app. Because the solutions were generated by specialists, they are a trustworthy source and provide a well-rounded learning experience.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>For some pupils, math can be a difficult subject. Because of the increased strain, it is especially difficult for pupils [&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":"Exercise 6.3 Class 12 Maths","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Free NCERT Solutions for Exercise 6.3 Class 12 Maths - Applications 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-exercise-6-3\/"},"categories":[19,32,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solution of Exercise 6.3 Class 12 Maths Chapter 6 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Free NCERT Solutions for Exercise 6.3 Class 12 Maths - 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