{"id":156392,"date":"2022-03-26T01:42:23","date_gmt":"2022-03-25T20:12:23","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/second-order-derivative-definition-and-solved-examples\/"},"modified":"2025-06-24T14:31:52","modified_gmt":"2025-06-24T09:01:52","slug":"second-order-derivative-definition-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/second-order-derivative\/","title":{"rendered":"Second Order Derivative \u2013 Definition and Solved Examples"},"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\/maths\/second-order-derivative\/#What_are_Second_Order_Derivatives\" title=\"What are Second Order Derivatives?\">What are Second Order 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\/maths\/second-order-derivative\/#Concavity\" title=\"Concavity\">Concavity<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/second-order-derivative\/#Point_of_Inflection\" title=\"Point of Inflection\">Point of Inflection<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/second-order-derivative\/#Second-Order_Derivative_Examples\" title=\"Second-Order Derivative Examples\">Second-Order Derivative Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/second-order-derivative\/#Second-Order_Derivatives_of_a_Parametric_Function\" title=\"Second-Order Derivatives of a Parametric Function\">Second-Order Derivatives of a Parametric Function<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Second_Order_Derivatives\"><\/span>What are Second Order Derivatives?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A second-order derivative is a derivative of a derivative. It is a measure of how quickly a function changes with respect to changes in its first derivative. Second-order derivatives are used in mathematical models to predict how a system will behave. Second Order Derivative \u2013 Definition and Solved Examples.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156391 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/second-order-derivative-definition-and-solved-examples.jpg\" alt=\"Second Order Derivative \u2013 Definition and Solved Examples\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/second-order-derivative-definition-and-solved-examples.jpg?v=1648239139 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/second-order-derivative-definition-and-solved-examples-300x212.jpg?v=1648239139 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Concavity\"><\/span>Concavity<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Concavity is a condition of a surface in which it curves inward. This can be seen in everyday objects such as cups, bowls, and in the surface of the Earth. The opposite of concavity is convexity, which is a condition of a surface in which it curves outward. Concavity is often associated with negative aspects such as sadness or depression, while convexity is often associated with positive aspects such as happiness or excitement.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Point_of_Inflection\"><\/span>Point of Inflection<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A <a href=\"https:\/\/en.wikipedia.org\/wiki\/Inflection_point\">point of inflection<\/a> (POI) is a point on a curve at which the curve changes from increasing to decreasing or from decreasing to increasing. The point of inflection is important in calculus because it is at this point that the derivative of the function is zero.<\/p>\n<p>The point of inflection can be found by using the second derivative test. The second derivative is zero at the point of inflection.<\/p>\n<p>For example, consider the curve y = x3. At the point of inflection, the second derivative is zero.<\/p>\n<p>The point of inflection can also be found by using the equation of the curve. The equation of the curve has a turning point at the point of inflection.<\/p>\n<p>For example, consider the curve y = x3 + 1. At the point of inflection, the curve has a turning point.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Second-Order_Derivative_Examples\"><\/span>Second-Order Derivative Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. Find the second derivative of y = x2.<\/p>\n<p>The second derivative of y = x2 is 2x.<\/p>\n<p>2. Find the second derivative of y = x3.<\/p>\n<p>The second derivative of y = x3 is 3&#215;2.<\/p>\n<p>3. Find the second derivative of y = x.<\/p>\n<p>The second derivative of y = x is 2x.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Second-Order_Derivatives_of_a_Parametric_Function\"><\/span>Second-Order Derivatives of a Parametric Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In calculus, the second-order derivative of a parametric function is the derivative of the derivative of the function. This is a measure of the rate of change of the rate of change of the function, and is also called the second derivative of the function.<\/p>\n<p>The second-order derivative can be used to determine whether a particular curve is a maximum or a minimum point on a graph. If the second derivative is negative at a point on the graph, then that point is a minimum; if the second derivative is positive at a point on the graph, then that point is a maximum.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What are Second Order Derivatives? A second-order derivative is a derivative of a derivative. It is a measure of how [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Second Order Derivative \u2013 Definition and Solved Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Second-Order Derivative topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/second-order-derivative\/"},"categories":[13],"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>Second Order Derivative \u2013 Definition and Solved Examples - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Second-Order Derivative topic of Maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/second-order-derivative\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Second Order Derivative \u2013 Definition and Solved Examples - 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