Question

A function f(x) satisfies the relation f(x + y) = f(x) + f(y) + xy (x + y) ∀ x, y ∈ R. If f′(0) = -1, then 

(A) f(x) is a polynomial function. 

(B) f(x) is an exponential function. 

(C) f(x) is twice differentiable for all x ∈ R. 

(D) f′(3) = 8.

Answer 1

Answer is (A), (C), (D)

f(x + y) = f(x) + f(y) + xy (x + y) f(0) = 0