Question

I hope you guys could help me out! Thank you.

Suppose f is a function that satisfies the equation f(x+y) = f(x) + f(y) + (x^2)y + x(y^2) for all real number x and y. Suppose also that the limit of [ f(x)/x) ] = 1 when x approaches 0.

a) Find f(0)
b) Find f'(0)
c) Find f'(x).

Answer 1

put x=y
u can find f(0)

Answer 2

Do you mean x = -y?