{"id":7997,"date":"2021-11-12T15:51:20","date_gmt":"2021-11-12T10:21:20","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7997"},"modified":"2021-11-14T01:01:58","modified_gmt":"2021-11-13T19:31:58","slug":"find-the-point-of-inflection-for-the-curve-y-x3-6x2-12x-5","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-point-of-inflection-for-the-curve-y-x3-6x2-12x-5\/","title":{"rendered":"Find the point of inflection for the curve y = \\(x^3 – 6x^2 + 12x + 5\\)."},"content":{"rendered":"

Solution :<\/h2>\n

y = \\(x^3 – 6x^2 + 12x + 5\\)<\/p>\n

y’ = \\(3x^2 – 12x + 12\\)<\/p>\n

y” = \\(6x – 12\\)<\/p>\n

y” = 0 \\(\\implies\\) 6x – 12 = 0<\/p>\n

\\(\\implies\\)\u00a0 x = 2<\/p>\n

Since, y” = 0 at x = 2,<\/p>\n

Hence the point of inflection<\/a> is 2.<\/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

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 inflection point of f(x) = \\(3x^4 \u2013 4x^3\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : y = \\(x^3 – 6x^2 + 12x + 5\\) y’ = \\(3x^2 – 12x + 12\\) y” = \\(6x – 12\\) y” = 0 \\(\\implies\\) 6x – 12 = 0 \\(\\implies\\)\u00a0 x = 2 Since, y” = 0 at x = 2, Hence the point of inflection is 2. Similar Questions Prove that …<\/p>\n

Find the point of inflection for the curve y = \\(x^3 – 6x^2 + 12x + 5\\).<\/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 the curve y = \\(x^3 - 6x^2 + 12x + 5\\).<\/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-the-curve-y-x3-6x2-12x-5\/\" \/>\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 the curve y = \\(x^3 - 6x^2 + 12x + 5\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : y = (x^3 – 6x^2 + 12x + 5) y’ = (3x^2 – 12x + 12) y” = (6x – 12) y” = 0 (implies) 6x – 12 = 0 (implies)\u00a0 x = 2 Since, y” = 0 at x = 2, Hence the point of inflection is 2. 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