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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Suppose f is a function that satisfies the equation

f(x + y) = f(x) + f(y) + x2y + xy2

for all real numbers x and y. Suppose also that

lim x 0 f ( x ) x = 1

(a) Find f(0).

(b) Find f'(0).

(c) Find f'(x).

(a)

To determine

To find: The value of the function f(0).

Explanation

Result used:

Definition of a derivative:

The definition of a derivative is f(x)=limh0f(x+h)f(x)h.

Calculation:

Given the function f(x+y)=f(x)+f(y)+x2y+xy2 and limx0f(x)x=1

(b)

To determine

To find: The value of the function f(0).

(c)

To determine

To find: The value of the function f(x)

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