Answered: 118. f(x) = - P(-1,4)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 31E

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Question

find the slope of the line tangent to the
graph of ƒ at P.
b. Determine an equation of the tangent line at P.
c. Plot the graph of ƒ and the tangent line at P.

Expert Solution

Step 1

The given function is $f (x) = \frac{4}{x^{2}}$ .

Obtain the derivative of the function as follows:

$f' (x) = \frac{d}{d x} (\frac{4}{x^{2}}) = - \frac{8}{x^{3}}$

Substitute x= -1 in the above equation.

$f' (- 1) = - \frac{8}{{(- 1)}^{3}} m = 8$

Thus, the slope is m=8

Step 2

Obtain the equation of tangent line as follows:

Substitute $(x_{1}, y_{1}) = (- 1, 4) a n d m = 8$ in $y - y_{1} = m (x - x_{1})$ .

$y - 4 = 8 (x + 1) y - 4 = 8 x + 8 y = 8 x + 8 + 4 y = 8 x + 12$

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