Answered: Find the slope m and an equation of the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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Question

Find the slope m and an equation of the tangent line to the graph of the function f at the specified point.

f(x) =

x²

x + 7

;

Expert Solution

Step 1

$G i v e n : f (x) = \frac{x^{2}}{x + 7} a t (1, \frac{1}{6})$

Step 2

$S l o p e \frac{d y}{d x} = \frac{d}{d x} (\frac{x^{2}}{x + 7}) = \frac{(x + 7) 2 x - (x^{2}) (1)}{{(x + 7)}^{2}} = \frac{2 x^{2} + 14 x - x^{2}}{{(x + 7)}^{2}} = \frac{x^{2} + 14 x}{{(x + 7)}^{2}}$

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