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A function y = f(x) and an x-value xo are given. f(x) = x + √√x; xo = 1 4 (a) Find a formula for the slope of the tangent line to the graph off at a general point xo. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. (a) Find a formula for the slope of the tangent line to the graph of f at a general point xo- The slope of the tangent line to f(x) at xo is given by Def 2.1.1: Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xo.f(xo)) is the line with equation y-f(xo) = man(x-xo) where man f(x)-f(xo) lim x-xo x-xo provided the limit exists. usingf(x) = x + √√x, we get Rewriting man = lim f(x)-f(xo), x-xo x-xo (x + √√x) - (x + √√xo x-xo (x +Và) xot vào x-xo mtan= lim- x-xo man lim x-xo (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. When xo 1, mtan =

A function y = f(x) and an x-value xo are given. f(x) = x + √√x; xo = 1 4 (a) Find a formula for the slope of the tangent line to the graph off at a general point xo. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. (a) Find a formula for the slope of the tangent line to the graph of f at a general point xo- The slope of the tangent line to f(x) at xo is given by Def 2.1.1: Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xo.f(xo)) is the line with equation y-f(xo) = man(x-xo) where man f(x)-f(xo) lim x-xo x-xo provided the limit exists. usingf(x) = x + √√x, we get Rewriting man = lim f(x)-f(xo), x-xo x-xo (x + √√x) - (x + √√xo x-xo (x +Và) xot vào x-xo mtan= lim- x-xo man lim x-xo (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. When xo 1, mtan =

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.2: Domain And Range
Problem 61SE: The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is...
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A function y = f(x) and an x-value xo are given. f(x) = x + √√x; Xo = 1 4 (a) Find a formula for the slope of the tangent line to the graph of f at a general point.xo. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. (a) Find a formula for the slope of the tangent line to the graph off at a general point xo- The slope of the tangent line to f(x) at xo is given by Def 2.1.1: Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xo.f(xo)) is the line with equation y-f(x) = man(x-xo) where man f(x)-f(xo). x-xo x-xo lim provided the limit exists. 4 using f(x) = x + √√x, we get Rewriting mtan= lim" x-xo O mtan f(x)-f(xo) x-xo (x+√√x) - (x + √√xo) x-xo lim- x-xo (x+√√x)-xo+ √√xo x-xo mtan lim- x-xo (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. When xo = 1, mtan =
Transcribed Image Text:A function y = f(x) and an x-value xo are given. f(x) = x + √√x; Xo = 1 4 (a) Find a formula for the slope of the tangent line to the graph of f at a general point.xo. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. (a) Find a formula for the slope of the tangent line to the graph off at a general point xo- The slope of the tangent line to f(x) at xo is given by Def 2.1.1: Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xo.f(xo)) is the line with equation y-f(x) = man(x-xo) where man f(x)-f(xo). x-xo x-xo lim provided the limit exists. 4 using f(x) = x + √√x, we get Rewriting mtan= lim" x-xo O mtan f(x)-f(xo) x-xo (x+√√x) - (x + √√xo) x-xo lim- x-xo (x+√√x)-xo+ √√xo x-xo mtan lim- x-xo (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. When xo = 1, mtan =
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