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Chapter 2: Q. 64 (page 185)

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that is perpendicular to the tangent line to f(x)=x4+1at x=2 and also passes through the point(-1,8)

Short Answer

Expert verified

The equation isy=-132x+25532

Step by step solution

01

Step 1. Given information

Given the functionf(x)=x4+1and the point(-1,8)

02

Calculate f'(2) using definition of derivative

Calculating, we get

f'(2)=limx鈫�2f(x)-f(2)x-2f'(2)=limx鈫�2x4+1-24+1x-2f'(2)=limx鈫�2x4-24x-2f'(2)=limx鈫�2(x-2)(x+2)x2+22(x-2)f'(2)=limx鈫�2(x+2)x2+22f'(2)=(2+2)22+22f'(2)=32

03

Use point slope form and calculate the form

Calculating, we get

Line is perpendicular to tangent line so m=-132

y-8=-132(x+1)y=-132x-132+8y=-132x+25532

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Most popular questions from this chapter

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The tangent line to f(x)=x2 atx=0

For each function fgraphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

Use the definition of the derivative to find f'for each function fin Exercises 39-54

role="math" localid="1648290170541" f(x)=x-1x+3

Use the differentiation rules developed in this section to find

the derivatives of the functions

f(x)=4-x7

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c)for each function f and value x=c in Exercises 23鈥�38.

27.f(x)=1-x3,x=-1
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