{"id":7995,"date":"2021-11-12T15:44:49","date_gmt":"2021-11-12T10:14:49","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7995"},"modified":"2021-11-14T01:02:10","modified_gmt":"2021-11-13T19:32:10","slug":"find-the-inflection-point-of-fx-3x4-4x3","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-inflection-point-of-fx-3x4-4x3\/","title":{"rendered":"Find the inflection point of f(x) = \\(3x^4 – 4x^3\\)."},"content":{"rendered":"

Solution :<\/h2>\n

f(x) = \\(3x^4 – 4x^3\\)<\/p>\n

f'(x) = \\(12x^3 – 12x^2\\)<\/p>\n

f'(x) = \\(12x^2(x – 1)\\)<\/p>\n

Now, f”(x) = \\(12(3x^2 – 2x)\\)<\/p>\n

f”(x) = 12x(3x – 2)<\/p>\n

f”(x) = 0\u00a0 \\(\\implies\\)\u00a0 x = 0, 2\/3<\/p>\n

Here, f”(x) = 0<\/p>\n

Thus, x = 0, 2\/3 are the inflection points<\/a>.<\/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

Find the point of inflection for f(x) = \\(x^4\\over 12\\) \u2013 \\(5x^3\\over 6\\) + \\(3x^2\\) + 7.<\/a><\/p>\n

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

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

Solution : f(x) = \\(3x^4 – 4x^3\\) f'(x) = \\(12x^3 – 12x^2\\) f'(x) = \\(12x^2(x – 1)\\) Now, f”(x) = \\(12(3x^2 – 2x)\\) f”(x) = 12x(3x – 2) f”(x) = 0\u00a0 \\(\\implies\\)\u00a0 x = 0, 2\/3 Here, f”(x) = 0 Thus, x = 0, 2\/3 are the inflection points. Similar Questions Prove that the function …<\/p>\n

Find the inflection point of f(x) = \\(3x^4 – 4x^3\\).<\/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 inflection point of f(x) = \\(3x^4 - 4x^3\\).<\/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-inflection-point-of-fx-3x4-4x3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the inflection point of f(x) = \\(3x^4 - 4x^3\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : f(x) = (3x^4 – 4x^3) f'(x) = (12x^3 – 12x^2) f'(x) = (12x^2(x – 1)) Now, f”(x) = (12(3x^2 – 2x)) f”(x) = 12x(3x – 2) f”(x) = 0\u00a0 (implies)\u00a0 x = 0, 2\/3 Here, f”(x) = 0 Thus, x = 0, 2\/3 are the inflection points. 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