MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
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
(1) f(x) is a polynomial function
(2) f(x) is an exponential function
(3) f(x) is twice differentiable for all x∈R
(4) f′(3)=8