   Chapter 2.7, Problem 28E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# If g(x) = x4 – 2, find g'(l) and use it to find an equation of the tangent line to the curve y = x4 – 2 at the point (1,–1).

To determine

To find: The derivative of the function g(x)=x42 at a=1 and obtain the equation of the tangent line to the curve y=x42 at the point (1, −1).

Explanation

Formula used:

The derivative of a function g at a number a, denoted by g(a) is,

g(a)=limxag(x)g(a)xa (1)

The equation of the tangent line to the curve y=g(x) at the point (a,g(a)) is,

yg(a)=g(a)(xa) (2)

Difference of squares formula: (a2b2)=(a+b)(ab)

Calculation:

Obtain the derivative of the function g(x) at a=1.

Compute g(1) by using the equation (1).

g(1)=limx1g(x)g(1)x1=limx1(x42)((1)42)x1=limx1(x42)(12)x1=limx1x42+1x1

=limx1x41x1=limx1(x2)2(1)2x1

Apply the difference of squares formula,

g(1)=limx<

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 