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

To find:The value of f(0) .

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

To find:The value of f'(0) .

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

To find:The value of f'(x) .

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 .

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