{"id":8052,"date":"2021-11-13T18:21:31","date_gmt":"2021-11-13T12:51:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8052"},"modified":"2021-11-14T01:00:01","modified_gmt":"2021-11-13T19:30:01","slug":"find-the-interval-in-which-fx-x2-2x-15-is-increasing-or-decreasing","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-interval-in-which-fx-x2-2x-15-is-increasing-or-decreasing\/","title":{"rendered":"Find the interval in which f(x) = \\(-x^2 – 2x + 15\\) is increasing or decreasing."},"content":{"rendered":"

Solution :<\/h2>\n

We have,\u00a0 f(x) = \\(-x^2 – 2x + 15\\)<\/p>\n

\\(\\implies\\) f'(x) = -2x – 2 = -2(x + 1)<\/p>\n

for f(x) to be increasing<\/a>, we must have<\/p>\n

f'(x) > 0<\/p>\n

-2(x + 1) > 0<\/p>\n

\\(\\implies\\) x + 1 < 0<\/p>\n

\\(\\implies\\) x < -1 \\(\\implies\\) x \\(\\in\\) \\((-\\infty, -1)\\).<\/p>\n

Thus f(x) is increasing on the interval \\((-\\infty, -1)\\).<\/p>\n

for f(x) to be decreasing<\/a>, we must have<\/p>\n

f'(x) > 0<\/p>\n

-2(x + 1) < 0<\/p>\n

\\(\\implies\\) x + 1 > 0<\/p>\n

\\(\\implies\\) x > -1 \\(\\implies\\) x \\(\\in\\) \\((-1, \\infty)\\).<\/p>\n

Thus f(x) is decreasing on the interval \\((-1, \\infty)\\).<\/p>\n

\n

Similar Questions<\/h3>\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

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

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

Solution : We have,\u00a0 f(x) = \\(-x^2 – 2x + 15\\) \\(\\implies\\) f'(x) = -2x – 2 = -2(x + 1) for f(x) to be increasing, we must have f'(x) > 0 -2(x + 1) > 0 \\(\\implies\\) x + 1 < 0 \\(\\implies\\) x < -1 \\(\\implies\\) x \\(\\in\\) \\((-\\infty, -1)\\). Thus f(x) is …<\/p>\n

Find the interval in which f(x) = \\(-x^2 – 2x + 15\\) is increasing or decreasing.<\/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 interval in which f(x) = \\(-x^2 - 2x + 15\\) is increasing or decreasing.<\/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-interval-in-which-fx-x2-2x-15-is-increasing-or-decreasing\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the interval in which f(x) = \\(-x^2 - 2x + 15\\) is increasing or decreasing.\" \/>\n<meta property=\"og:description\" content=\"Solution : We have,\u00a0 f(x) = (-x^2 – 2x + 15) (implies) f'(x) = -2x – 2 = -2(x + 1) for f(x) to be increasing, we must have f'(x) > 0 -2(x + 1) > 0 (implies) x + 1 < 0 (implies) x < -1 (implies) x (in) ((-infty, -1)). 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