# The value of f ( 0 ) .

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 2, Problem 13P

(a)

To determine

Expert Solution

## Answer to Problem 13P

The value of f(0) is 0 .

### Explanation of Solution

Given information:

The given function f(x+y)=f(x)+f(y)+x2y+xy2 is true for all real x and y .

Calculation:

Substitute 0 for x in above given equation.

f(x+y)=f(x)+f(y)+x2y+xy2f(0+y)=f(0)+f(y)+02y+0y2f(y)=f(0)+f(y)f(0)=0

Therefore, the value of f(0) is 0 .

(b)

To determine

Expert Solution

## Answer to Problem 13P

The value of f'(0) is 1 .

### Explanation of Solution

Given information:

The given function f(x+y)=f(x)+f(y)+x2y+xy2 is true for all real x and y .

Calculation:

The value of f'(x) for all xR .

f'(x)=1x2

Substitute 0 for x in above given equation.

f'(0)=102=1

Therefore, the value of f'(0) is 1 .

(c)

To determine

Expert Solution

## Answer to Problem 13P

The value of f'(x) is 1x2 .

### Explanation of Solution

Given information:

The given function f(x+y)=f(x)+f(y)+x2y+xy2 is true for all real x and y .

Calculation:

The value of f'(x) for all xR .

f'(x)=1x2

Therefore, the value of f'(x) is 1x2 .

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!