{"id":8008,"date":"2021-11-12T16:34:20","date_gmt":"2021-11-12T11:04:20","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8008"},"modified":"2021-11-14T01:01:45","modified_gmt":"2021-11-13T19:31:45","slug":"find-the-point-of-inflection-for-fx-x4over-12-5x3over-6-3x2-7","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-point-of-inflection-for-fx-x4over-12-5x3over-6-3x2-7\/","title":{"rendered":"Find the point of inflection for f(x) = \\(x^4\\over 12\\) – \\(5x^3\\over 6\\) + \\(3x^2\\) + 7."},"content":{"rendered":"

Solution :<\/h2>\n

f(x) = \\(x^4\\over 12\\) – \\(5x^3\\over 6\\) + \\(3x^2\\) + 7.<\/p>\n

f'(x) = \\(x^3\\over 3\\) – \\(5x^2\\over 2\\) + 6x<\/p>\n

f”(x) = \\(x^2\\) – 5x + 6<\/p>\n

Since, f”(x) = 0 at point of inflection<\/a>.<\/p>\n

\\(\\implies\\) \\(x^2\\) – 5x + 6 = 0<\/p>\n

\\(\\implies\\) x = 2 and x = 3<\/p>\n

Hence, points of inflection are 2 and 3.<\/p>\n

\n

Similar Questions<\/h3>\n

Prove that the function f(x) = \\(x^3 \u2013 3x^2 + 3x \u2013 100\\) is increasing on R<\/a><\/p>\n

Separate \\([0, {\\pi\\over 2}]\\) into subintervals in which f(x) = sin 3x is increasing or decreasing.<\/a><\/p>\n

Prove that \\(f(\\theta)\\) = \\({4sin \\theta\\over 2 + cos\\theta} \u2013 \\theta\\) is an increasing function of \\(\\theta\\) in \\([0, {\\pi\\over 2}]\\).<\/a><\/p>\n

Find the point of inflection for the curve y = \\(x^3 \u2013 6x^2 + 12x + 5\\).<\/a><\/p>\n

Find the inflection point of f(x) = \\(3x^4 \u2013 4x^3\\).<\/a><\/p>\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : f(x) = \\(x^4\\over 12\\) – \\(5x^3\\over 6\\) + \\(3x^2\\) + 7. f'(x) = \\(x^3\\over 3\\) – \\(5x^2\\over 2\\) + 6x f”(x) = \\(x^2\\) – 5x + 6 Since, f”(x) = 0 at point of inflection. \\(\\implies\\) \\(x^2\\) – 5x + 6 = 0 \\(\\implies\\) x = 2 and x = 3 Hence, points …<\/p>\n

Find the point of inflection for f(x) = \\(x^4\\over 12\\) – \\(5x^3\\over 6\\) + \\(3x^2\\) + 7.<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[66,43],"tags":[],"yoast_head":"\nFind the point of inflection for f(x) = \\(x^4\\over 12\\) - \\(5x^3\\over 6\\) + \\(3x^2\\) + 7.<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/find-the-point-of-inflection-for-fx-x4over-12-5x3over-6-3x2-7\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the point of inflection for f(x) = \\(x^4\\over 12\\) - \\(5x^3\\over 6\\) + \\(3x^2\\) + 7.\" \/>\n<meta property=\"og:description\" content=\"Solution : f(x) = (x^4over 12) – (5x^3over 6) + (3x^2) + 7. f'(x) = (x^3over 3) – (5x^2over 2) + 6x f”(x) = (x^2) – 5x + 6 Since, f”(x) = 0 at point of inflection. (implies) (x^2) – 5x + 6 = 0 (implies) x = 2 and x = 3 Hence, points … Find the point of inflection for f(x) = (x^4over 12) – (5x^3over 6) + (3x^2) + 7. 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