{"id":69080,"date":"2023-09-12T20:58:00","date_gmt":"2023-09-12T15:28:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69080"},"modified":"2023-11-09T14:12:45","modified_gmt":"2023-11-09T08:42:45","slug":"rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/","title":{"rendered":"RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2 (2023-24)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-120849\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-18-Exercise-18.2.jpg\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-18-Exercise-18.2.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-18-Exercise-18.2-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2<\/strong>: RD Sharma&#8217;s book solution uses a structured approach to better understand and understand concepts. These RD Sharma Class 12 solutions are designed by a group of experts in the field to eliminate students\u2019 doubts. You can easily download the solutions from the link provided below. The RD Sharma solution is very helpful.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-12-solutions\/\" target=\"_blank\" rel=\"noopener\"><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;RD Sharma Solutions for Class 12&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:16897,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;17&quot;:1}\">RD Sharma Solutions for Class 12 Maths All Chapters\u00a0<\/span><\/a>\u00a0<\/li>\n<\/ul>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 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\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69e8dd9558271\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" 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: #000000;color:#000000\" 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-69e8dd9558271\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#download-rd-sharma-solutions-class-12-maths-chapter-18-exercise-182-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2 PDF:\">Download RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2 PDF:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#access-rd-sharma-solutions-class-12-maths-chapter-18-exercise-182\" title=\"Access RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2\">Access RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#rd-sharma-solutions-class-12-maths-chapter-18-exercise-182-important-topics-from-the-chapter\" title=\"RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2: Important Topics From The Chapter\">RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2: Important Topics From The Chapter<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#faq-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-182\" title=\"FAQ: RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2\">FAQ: RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#what-are-the-important-topics-included-in-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-182\" title=\"What are the important topics included in RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2?\">What are the important topics included in RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#can-i-download-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-181-pdf-free\" title=\"Can I download RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.1 PDF free?\">Can I download RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.1 PDF free?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#what-are-the-benefits-of-studying-from-rd-sharma-solutions-class-12\" title=\"What are the benefits of studying from RD Sharma Solutions Class 12?\">What are the benefits of studying from RD Sharma Solutions Class 12?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#can-i-open-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-182-pdf-on-my-smartphone\" title=\"Can I open RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2 PDF on my smartphone?\">Can I open RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2 PDF on my smartphone?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/#is-rd-sharma-enough-for-the-class-12-exams\" title=\"Is RD Sharma enough for the Class 12 Exams?\">Is RD Sharma enough for the Class 12 Exams?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-18-exercise-182-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2 PDF:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-18-Ex-18.2-1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-18-Ex-18.2-1.pdf\">RD-Sharma-Solutions-Class-12-Maths-Chapter-18-Ex-18.2<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-12-maths-chapter-18-exercise-182\"><\/span>Access RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Find the points of local maxima or local minima, if any, of the following functions using the first derivative test. Also, find the local maximum or local minimum values, as the case may be:<\/strong><\/p>\n<p><strong>1. f (x) = (x \u2013 5)<sup>4<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given f (x) = (x \u2013 5)<sup>4<\/sup><\/p>\n<p>Differentiate with respect to x<\/p>\n<p>f\u2019(x) = 4(x \u2013 5)<sup>3<\/sup><\/p>\n<p>For local maxima and minima<\/p>\n<p>f\u2018(x) = 0<\/p>\n<p>= 4(x \u2013 5)<sup>3<\/sup>\u00a0= 0<\/p>\n<p>= x \u2013 5 = 0<\/p>\n<p>x = 5<\/p>\n<p>f\u2018(x) changes from negative to positive as it passes through 5.<\/p>\n<p>So, x = 5 is the point of local minima<\/p>\n<p>Thus, the local minima value is f (5) = 0<\/p>\n<p><strong>2. f (x) = x<sup>3<\/sup>\u00a0\u2013 3x<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given, f (x) = x<sup>3<\/sup>\u00a0\u2013 3x<\/p>\n<p>Differentiate with respect to x then we get,<\/p>\n<p>f\u2019 (x) = 3x<sup>2<\/sup>\u00a0\u2013 3<\/p>\n<p>Now, f\u2018(x) =0<\/p>\n<p>3x<sup>2<\/sup>\u00a0= 3\u00a0\u21d2\u00a0x = \u00b11<\/p>\n<p>Again differentiate f\u2019(x) = 3x<sup>2<\/sup>\u00a0\u2013 3<\/p>\n<p>f\u2019\u2019(x)= 6x<\/p>\n<p>f\u2019\u2019(1)= 6 &gt; 0<\/p>\n<p>f\u2019\u2019 (\u2013 1)= \u2013 6 &lt; 0<\/p>\n<p>By the second derivative test, x = 1 is a point of local minima and local minimum value of f at<\/p>\n<p>x = 1 is f (1) = 1<sup>3<\/sup>\u00a0\u2013 3 = 1 \u2013 3 = \u2013 2<\/p>\n<p>However, x = \u2013 1 is a point of the local maxima and local maxima value of f at<\/p>\n<p>x = \u2013 1 is<\/p>\n<p>f (\u2013 1) = (\u2013 1)<sup>3<\/sup>\u00a0\u2013 3(\u2013 1)<\/p>\n<p>= \u2013 1 + 3<\/p>\n<p>= 2<\/p>\n<p>Hence, the value of minima is \u2013 2 and maxima is 2.<\/p>\n<p><strong>3. f (x) = x<sup>3<\/sup>\u00a0(x \u2013 1)<sup>2<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given, f(x) = x<sup>3<\/sup>(x \u2013 1)<sup>2<\/sup><\/p>\n<p>Differentiate with respect to x, we get,<\/p>\n<p>f \u2018(x) = 3x<sup>2<\/sup>(x \u2013 1)<sup>2<\/sup>\u00a0+ 2x<sup>3<\/sup>(x \u2013 1)<\/p>\n<p>= (x \u2013 1) (3x<sup>2<\/sup>(x \u2013 1) + 2x<sup>3<\/sup>)<\/p>\n<p>= (x \u2013 1) (3x<sup>3<\/sup>\u00a0\u2013 3x<sup>2<\/sup>\u00a0+ 2x<sup>3<\/sup>)<\/p>\n<p>= (x \u2013 1) (5x<sup>3<\/sup>\u00a0\u2013 3x<sup>2<\/sup>)<\/p>\n<p>= x<sup>2<\/sup>\u00a0(x \u2013 1) (5x \u2013 3)<\/p>\n<p>For all maxima and minima,<\/p>\n<p>f \u2019(x) = 0<\/p>\n<p>= x<sup>2<\/sup>(x \u2013 1) (5x \u2013 3) = 0<\/p>\n<p>By solving the above equation, we get<\/p>\n<p>x =0, 1,\u00a03\/5<\/p>\n<p>At x =\u00a03\/5,\u00a0f\u2019(x) changes from negative to positive<\/p>\n<p>Since x = 3\/5 is a point of Minima<\/p>\n<p>At x =1, f\u2018(x) changes from positive to negative<\/p>\n<p>Since x =1 is the point of maxima.<\/p>\n<p><strong>4. f (x) = (x \u2013 1) (x + 2)<sup>2<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given, f(x) = (x \u2013 1) (x + 2)<sup>2<\/sup><\/p>\n<p>Differentiate with respect to x, we get,<\/p>\n<p>f\u2018(x) = (x + 2)<sup>2<\/sup>\u00a0+ 2(x \u2013 1)(x + 2)<\/p>\n<p>= (x + 2) (x + 2 + 2x \u2013 2)<\/p>\n<p>= (x + 2) (3x)<\/p>\n<p>For all maxima and minima,<\/p>\n<p>f\u2019(x) = 0<\/p>\n<p>(x + 2) (3x) = 0<\/p>\n<p>By solving the above equation, we get<\/p>\n<p>x = 0, \u2013 2<\/p>\n<p>At x =\u00a0\u2013 2, f\u2019(x) changes from positive to negative<\/p>\n<p>Since x = \u2013 2 is a point of Maxima<\/p>\n<p>At x = 0, f\u2018(x) changes from negative to positive<\/p>\n<p>Since x = 0 is a point of Minima.<\/p>\n<p>Hence, local min value = f (0) = \u2013 4<\/p>\n<p>Local max value = f (\u2013 2) = 0.<\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 18\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-18-maxima-and-minima-image-1.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 18 Maxima and Minima Image 1\" \/><\/p>\n<p>Therefore x = 0, now for the values close to x = 0 and to the left of 0, f'(x) &gt; 0<\/p>\n<p>Also for values x = 0 and to the right of 0, f\u2019(x) &lt; 0<\/p>\n<p>Therefore, by the first derivative test, x = 0 is a point of local maxima and the local minima value of f (x) is \u00bd.<\/p>\n<p><strong>6. f (x) = x<sup>3<\/sup>\u00a0\u2013 6x<sup>2<\/sup>\u00a0+ 9x +15<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given, f(x) = x<sup>3<\/sup>\u00a0\u2013 6x<sup>2<\/sup>\u00a0+ 9x + 15<\/p>\n<p>Differentiate with respect to x, we get, f\u2018(x) = 3x<sup>2<\/sup>\u00a0\u2013 12x + 9 = 3(x<sup>2<\/sup>\u00a0\u2013 4x + 3)<\/p>\n<p>= 3 (x \u2013 3) (x \u2013 1)<\/p>\n<p>For all maxima and minima,<\/p>\n<p>f\u2019(x) = 0<\/p>\n<p>= 3(x \u2013 3) (x \u2013 1) = 0<\/p>\n<p>= x = 3, 1<\/p>\n<p>At x =\u00a01, f\u2019(x) changes from positive to negative<\/p>\n<p>Since x = 1 is a point of Maxima<\/p>\n<p>At x = 3, f\u2018(x) changes from negative to positive<\/p>\n<p>Since x = 3 is a point of Minima.<\/p>\n<p>Hence, local maxima value f (1) =\u00a0(1)<sup>3<\/sup>\u00a0\u2013 6(1)<sup>2<\/sup>\u00a0+ 9(1) + 15 = 19<\/p>\n<p>Local minima value f (3) =\u00a0(3)<sup>3<\/sup>\u00a0\u2013 6(3)<sup>2<\/sup>\u00a0+ 9(3) + 15 = 15<\/p>\n<p><strong>7. f (x) = sin 2x, 0 &lt; x &lt; \u03c0<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given f (x) = sin 2x<\/p>\n<p>Differentiate w.r.t x, we get<\/p>\n<p>f'(x) = 2 cos 2x, 0 &lt; x &lt; \u03c0<\/p>\n<p>For the point of local maxima and minima, f\u2019(x) = 0<\/p>\n<p>2 cos 2x = 0<\/p>\n<p>cos 2x = 0<\/p>\n<p>2x = \u03c0\/2, 3\u03c0\/2<\/p>\n<p>x = \u03c0\/4, 3\u03c0\/4<\/p>\n<p>Now, at x = \u03c0\/4, f\u2019(x) changes from positive to negative<\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 18\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-18-maxima-and-minima-image-2.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 18 Maxima and Minima Image 2\" \/><\/p>\n<hr \/>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-12-maths-chapter-18-exercise-182-important-topics-from-the-chapter\"><\/span>RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2: Important Topics From The Chapter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Some of the crucial topics of <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 12 Maths Chapter 18<\/a> Exercise 18.2 are enlisted here.<\/p>\n<ul>\n<li>Maximum and minimum values of a function in its domain<\/li>\n<li>Definition and meaning of maximum<\/li>\n<li>Definition and meaning of minimum<\/li>\n<li>Local maxima<\/li>\n<li>Local minima<\/li>\n<li>First derivative test for local maxima and minima<\/li>\n<li>Higher-order derivative test<\/li>\n<li>Theorem and algorithm based on higher derivative test<\/li>\n<li>Point of inflection<\/li>\n<li>Point of inflection<\/li>\n<li>Properties of maxima and minima<\/li>\n<li>Maximum and minimum values in a closed interval<\/li>\n<li>Applied problems on maxima and minima<\/li>\n<\/ul>\n<p>We have included all the information regarding\u00a0<a href=\"http:\/\/cbseacademic.nic.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a> RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2. If you have any queries feel free to ask in the comment section.\u00a0<\/p>\n<h3><span class=\"ez-toc-section\" id=\"faq-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-182\"><\/span>FAQ: RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630077898724\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-important-topics-included-in-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-182\"><\/span>What are the important topics included in RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can refer to the above article to know important topics included in RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630077914370\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-download-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-181-pdf-free\"><\/span>Can I download RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.1 PDF free?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, you can download RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.1 PDF for free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630077919264\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-benefits-of-studying-from-rd-sharma-solutions-class-12\"><\/span>What are the benefits of studying from RD Sharma Solutions Class 12?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>By practicing these solutions, students can earn higher academic grades. Our experts solve these solutions with utmost accuracy to help students in their studies.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630077920496\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-open-rd-sharma-solutions-class-12-maths-chapter-18-maxima-and-minima-exercise-182-pdf-on-my-smartphone\"><\/span>Can I open RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2 PDF on my smartphone?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, you can open RD Sharma Solutions Class 12 Maths Chapter 18 Maxima and Minima Exercise 18.2 on any device.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630077921528\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-rd-sharma-enough-for-the-class-12-exams\"><\/span>Is RD Sharma enough for the Class 12 Exams?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>RD Sharma has a variety of questions for class 12 board exams.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2: RD Sharma&#8217;s book solution uses a structured approach to better understand and understand concepts. These RD Sharma Class 12 solutions are designed by a group of experts in the field to eliminate students\u2019 doubts. You can easily download the solutions from the link provided below. &#8230; <a title=\"RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2 (2023-24)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-18-exercise-18-2\/\" aria-label=\"More on RD Sharma Solutions Class 12 Maths Chapter 18 Exercise 18.2 (2023-24)\">Read more<\/a><\/p>\n","protected":false},"author":244,"featured_media":120849,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73716,73411,2985,73410],"tags":[3429,73223,73664,76770],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69080"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=69080"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69080\/revisions"}],"predecessor-version":[{"id":505066,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69080\/revisions\/505066"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/120849"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69080"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69080"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69080"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}