# To use a CAS to differentiate the given function. ### Single Variable Calculus: Concepts...

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

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

Expert Solution

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

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. ### Have a homework question?

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