   Chapter 4.5, Problem 66E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Finding Relative Extrema In Exercises 65-68, find all relative extrema of the function. Use a graphing utility to verify your result. See Example 6. y = ln 2 x − 2 x 2

To determine

To calculate: The relative extrema of the function y=ln 2x2x2.

Explanation

Given Information:

The provided function is y=ln 2x2x2.

Formula used:

Rules for derivatives:

Sum rule of derivative:

(f(x)+g(x))'=f'(x)+g'(x)

Derivative of function f(x)=ln x is,

ddxlnx=1x

Constant multiple rule is f'(cx)=cf(x) where c is constant.

Derivative of function y=xn using power rule is dydx=nxn1.

Calculation:

Consider the function y=ln 2x2x2.

First, evaluate the first derivative of the function y=ln 2x2x2.

dydx=ddx(ln 2x2x2)

Apply the sum rule,

ddx(ln 2x2x2)=ddx(ln 2x)ddx(2x2)=ddx(ln 2)+ddx(ln x)ddx(2x2)=0+1x4x=1x4x

Hence, the first derivative of the function is dydx=1x4x.

Now, set the derivative equal to 0.

1x4x=01x=4x4x2=1x2=14

Further solve as,

x=14x=±12

Hence, the only critical numbers are x=12,x=12, but x=12 is not in the domain of y

### 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

#### Sketch the graphs of the equations in Exercises 512. xy=4

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Find y and y. y=1(1+tanx)2

Single Variable Calculus: Early Transcendentals, Volume I

#### In Problems 19-44, factor completely. 42.

Mathematical Applications for the Management, Life, and Social Sciences

#### Evaluate the indefinite integral. (lnx)2xdx

Single Variable Calculus: Early Transcendentals

#### Define the validity of measurement and explain why and how it is measured.

Research Methods for the Behavioral Sciences (MindTap Course List) 