{"id":20266,"date":"2024-04-15T05:50:37","date_gmt":"2024-04-15T05:50:37","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20266"},"modified":"2024-04-15T05:50:37","modified_gmt":"2024-04-15T05:50:37","slug":"equation-of-the-line-normal-to-function-textfleft-textx-right-left-textx-8-rightfrac23-1-at-p0-5-is-a-y-3x-5-b-y-3x-5-c-3y-x-15-d","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/equation-of-the-line-normal-to-function-textfleft-textx-right-left-textx-8-rightfrac23-1-at-p0-5-is-a-y-3x-5-b-y-3x-5-c-3y-x-15-d\/","title":{"rendered":"Equation of the line normal to function $${\\text{f}}\\left( {\\text{x}} \\right) = {\\left( {{\\text{x}} – 8} \\right)^{\\frac{2}{3}}} + 1$$ at P(0, 5) is A. y = 3x – 5 B. y = 3x + 5 C. 3y = x + 15 D. 3y = x – 15"},"content":{"rendered":"

[amp_mcq option1=”y = 3x – 5″ option2=”y = 3x + 5″ option3=”3y = x + 15″ option4=”3y = x – 15″ correct=”option3″]<\/p>\n

The equation of the line normal to the function $f(x) = \\left(x – 8\\right)^{2\/3} + 1$ at $P(0, 5)$ is $3y = x – 15$.<\/p>\n

The slope of the tangent line to the function $f(x)$ at $x = a$ is given by $f'(a)$. The slope of the normal line to the function $f(x)$ at $x = a$ is $-\\frac{1}{f'(a)}$.<\/p>\n

In this case, $f'(x) = \\frac{2}{3} \\left(x – 8\\right)^{-1\/3}$. Therefore, the slope of the tangent line to the function $f(x)$ at $x = 0$ is $2$.<\/p>\n

The normal line to the function $f(x)$ at $x = 0$ has a slope of $-\\frac{1}{2}$. The equation of the line with slope $-\\frac{1}{2}$ and passing through the point $(0, 5)$ is $y – 5 = -\\frac{1}{2}(x – 0)$, which simplifies to $3y = x – 15$.<\/p>\n

Therefore, the equation of the line normal to the function $f(x) = \\left(x – 8\\right)^{2\/3} + 1$ at $P(0, 5)$ is $3y = x – 15$.<\/p>\n","protected":false},"excerpt":{"rendered":"

[amp_mcq option1=”y = 3x – 5″ option2=”y = 3x + 5″ option3=”3y = x + 15″ option4=”3y = x – 15″ correct=”option3″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[690],"tags":[],"class_list":["post-20266","post","type-post","status-publish","format-standard","hentry","category-calculus","no-featured-image-padding"],"yoast_head":"\nEquation of the line normal to function $${\\text{f}}\\left( {\\text{x}} \\right) = {\\left( {{\\text{x}} - 8} \\right)^{\\frac{2}{3}}} + 1$$ at P(0, 5) is A. y = 3x - 5 B. y = 3x + 5 C. 3y = x + 15 D. 3y = x - 15<\/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:\/\/exam.pscnotes.com\/mcq\/equation-of-the-line-normal-to-function-textfleft-textx-right-left-textx-8-rightfrac23-1-at-p0-5-is-a-y-3x-5-b-y-3x-5-c-3y-x-15-d\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equation of the line normal to function $${\\text{f}}\\left( {\\text{x}} \\right) = {\\left( {{\\text{x}} - 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8} \\right)^{\\frac{2}{3}}} + 1$$ at P(0, 5) is A. y = 3x - 5 B. y = 3x + 5 C. 3y = x + 15 D. 3y = x - 15","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/equation-of-the-line-normal-to-function-textfleft-textx-right-left-textx-8-rightfrac23-1-at-p0-5-is-a-y-3x-5-b-y-3x-5-c-3y-x-15-d\/","og_locale":"en_US","og_type":"article","og_title":"Equation of the line normal to function $${\\text{f}}\\left( {\\text{x}} \\right) = {\\left( {{\\text{x}} - 8} \\right)^{\\frac{2}{3}}} + 1$$ at P(0, 5) is A. y = 3x - 5 B. y = 3x + 5 C. 3y = x + 15 D. 3y = x - 15","og_description":"[amp_mcq option1=”y = 3x – 5″ option2=”y = 3x + 5″ option3=”3y = x + 15″ option4=”3y = x – 15″ correct=”option3″]","og_url":"https:\/\/exam.pscnotes.com\/mcq\/equation-of-the-line-normal-to-function-textfleft-textx-right-left-textx-8-rightfrac23-1-at-p0-5-is-a-y-3x-5-b-y-3x-5-c-3y-x-15-d\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-04-15T05:50:37+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/equation-of-the-line-normal-to-function-textfleft-textx-right-left-textx-8-rightfrac23-1-at-p0-5-is-a-y-3x-5-b-y-3x-5-c-3y-x-15-d\/","url":"https:\/\/exam.pscnotes.com\/mcq\/equation-of-the-line-normal-to-function-textfleft-textx-right-left-textx-8-rightfrac23-1-at-p0-5-is-a-y-3x-5-b-y-3x-5-c-3y-x-15-d\/","name":"Equation of the line normal to function $${\\text{f}}\\left( {\\text{x}} \\right) = {\\left( {{\\text{x}} - 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