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MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let f(x+y)=f(x)+f(y)f(x+y) = f(x) + f(y) and f(x)=x2g(x)f(x) = x^2 g(x) for all x,y∈Rx, y \in \mathbb{R}, where g(x)g(x) is continuous function. Then f′(x)f'(x) is equal to (a) g′(x)g'(x) (b) g(0)g(0) (c) g(0)+g(x)g(0) + g(x) (d) 0

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