{"id":154700,"date":"2022-03-25T23:49:36","date_gmt":"2022-03-25T18:19:36","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/mean-value-theorem-definition-geometrical-representation-and-solved-examples\/"},"modified":"2022-12-22T21:52:25","modified_gmt":"2022-12-22T16:22:25","slug":"mean-value-theorem-definition-geometrical-representation-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/mean-value-theorem\/","title":{"rendered":"Mean Value Theorem &#8211; Definition, Geometrical Representation 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\/mean-value-theorem\/#What_is_The_Mean_Value_Theorem\" title=\"What is The Mean Value Theorem?\">What is The Mean Value Theorem?<\/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\/mean-value-theorem\/#Geometrical_Representation_of_Mean_Value_Theorem\" title=\"Geometrical Representation of Mean Value Theorem\">Geometrical Representation of Mean Value Theorem<\/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\/mean-value-theorem\/#What_is_The_Mean_Value_Theorem_for_Integrals\" title=\"What is The Mean Value Theorem for Integrals?\">What is The Mean Value Theorem for Integrals?<\/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\/mean-value-theorem\/#Cauchy_Mean_Value_Theorem\" title=\"Cauchy Mean Value Theorem\">Cauchy Mean Value Theorem<\/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\/mean-value-theorem\/#Mean_Value_Theorem_for_Integral_Problems\" title=\"Mean Value Theorem for Integral Problems\">Mean Value Theorem for Integral Problems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mean-value-theorem\/#Here_you_can_see_a_mean_value_theorem_for_integrals_problems_with_solutions\" title=\"Here, you can see a mean value theorem for integrals problems with solutions.\">Here, you can see a mean value theorem for integrals problems with solutions.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mean-value-theorem\/#Solved_Example\" title=\"Solved Example\">Solved Example<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/mean-value-theorem\/#Facts\" title=\"Facts\">Facts<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_The_Mean_Value_Theorem\"><\/span>What is The Mean Value Theorem?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The mean value theorem states that for a given function, there is a value that exists between any two given points on the function&#8217;s graph. This value is the average of the two points.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154699 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/mean-value-theorem-definition-geometrical-representation-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/mean-value-theorem-definition-geometrical-representation-and-solved-examples.jpg?v=1648232370 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/mean-value-theorem-definition-geometrical-representation-and-solved-examples-300x212.jpg?v=1648232370 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Geometrical_Representation_of_Mean_Value_Theorem\"><\/span>Geometrical Representation of Mean Value Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Mean Value Theorem states that there is a point on the function between the two points given that the function is continuous on the closed interval. This point is the average value of the function on the interval.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_The_Mean_Value_Theorem_for_Integrals\"><\/span>What is The Mean Value Theorem for Integrals?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Mean Value Theorem for Integrals is a theorem that states that there is a point between two given points on a function where the value of the function is equal to the average value of the function over the interval between the two points.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cauchy_Mean_Value_Theorem\"><\/span>Cauchy Mean Value Theorem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Cauchy Mean Value Theorem states that if is a function that is continuous on the closed interval and differentiable on the open interval then there exists a point in the open interval such that .<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Mean_Value_Theorem_for_Integral_Problems\"><\/span>Mean Value Theorem for Integral Problems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If is a function and is an interval in the real numbers, then<\/p>\n<p>provided that the function is continuous on .<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Here_you_can_see_a_mean_value_theorem_for_integrals_problems_with_solutions\"><\/span>Here, you can see a mean value theorem for integrals problems with solutions.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Mean Value Theorem for Integrals states that if is a continuous function on the interval then there exists a point within the interval at which the derivative of is equal to .<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Example\"><\/span>Solved Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The following example will help you understand how to find the zeros of a function.<\/p>\n<p>Find the zeros of the function \\(f(x) = x^3 &#8211; 2x^2 + 5x &#8211; 4\\)<\/p>\n<p>There are three zeros of this function &#8211; at \\(x = -1, x = 2, x = 4\\).<\/p>\n<h2><\/h2>\n<p>H\u00e9tf\u0151n, a Fidesz frakci\u00f3vezet\u0151-helyettes\u00e9nek bejelent\u00e9se szerint a korm\u00e1nyp\u00e1rtok elfogadt\u00e1k a Jobbikt\u00f3l kapott ind\u00edtv\u00e1nyt, miszerint a Magyar Nemzeti Bank (MNB) eln\u00f6ke, illetve aleln\u00f6kei felett a jegybanki fel\u00fcgyel\u0151bizotts\u00e1g gyakorolja a fel\u00fcgyeletet.<\/p>\n<p>A frakci\u00f3vezet\u0151-helyettes szerint a Jobbik ind\u00edtv\u00e1nya elfogad\u00e1s\u00e1val az Orsz\u00e1ggy\u0171l\u00e9s kimondta, hogy a jegybanki fel\u00fcgyeletet nem a korm\u00e1ny, hanem a parlament gyakorolja.<\/p>\n<p>A korm\u00e1nyp\u00e1rti t\u00f6bbs\u00e9g azonban \u00fagy l\u00e1tja, hogy az MNB eln\u00f6keinek \u00e9s aleln\u00f6keinek felett a jegybanki fel\u00fcgyel\u0151bizotts\u00e1g gyakorolja a fel\u00fcgyeletet, az Orsz\u00e1ggy\u0171l\u00e9s nem<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Facts\"><\/span>Facts<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>About the Detroit Lions<\/p>\n<p>The Detroit Lions are a professional football team in the National Football League (NFL). The team is based in Detroit, Michigan, and plays its home games at Ford Field. The Detroit Lions were founded in 1929 as the Portsmouth Spartans and are one of the oldest franchises in the NFL. The team was renamed the Detroit Lions in 1934. The Detroit Lions have won four NFL championships, the last of which came in 1957. The Detroit Lions are also a member of the NFC (National Football Conference) North division.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is The Mean Value Theorem? The mean value theorem states that for a given function, there is a value [&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":"Mean Value Theorem - Definition, Geometrical Representation and Solved Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Mean Value Theorem topic of Maths in details explained by subject experts on infinitylearn.com. 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