BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.4, Problem 88E

a.

To determine

To use a CAS to differentiate the given function.

Expert Solution

Answer to Problem 88E

  3x41x4x+1x4+x+1(x4+x+1)2

Explanation of Solution

Given:

The given function is f(x)=x4x+1x4+x+1

Calculation:

In wolfram alpha typing the following things give-

  der(sqrt((x4x+1)/(x4+x+1)))

The results will be-

  =(4x31)(x4+x+1)(4x3+1)(x4x+1)(x4+x+1)22x4x+1x4+x+1

They usually give the most simplified answer on first time and sometimes list alternate forms below. So, there is no real need to use simplify command.

The alternate form might be considered more helpful for finding zeroes.

  3x41x4x+1x4+x+1(x4+x+1)2

b.

To determine

To find the location where graph of f have horizontal tangents.

Expert Solution

Answer to Problem 88E

  x=±134

Explanation of Solution

Given:

The given function is f(x)=x4x+1x4+x+1

Calculation:

The horizontal tangents occur if the derivative of the function is zero.

  3x41x4x+1x4+x+1(x4+x+1)2=03x41=0x4=13x=±134

c.

To determine

To graph f and f' on the same curve.

Expert Solution

Explanation of Solution

Given:

The given function is f(x)=x4x+1x4+x+1

Calculation:

The f(x) is the black curve.

And f'(x) is the blue curve.

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 3.4, Problem 88E

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