Let be continuous and differentiable function for all reals and

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

Problem

Let f(x)f(x) be continuous and differentiable function for all reals and f(x+y)=f(x)−3xy+f(y)f(x+y) = f(x) - 3xy + f(y) . If lim⁡h→0f(h)h=7\lim_{h \to 0} \frac{f(h)}{h} = 7 , then the value of f′(x)f'(x) is (1) −3x-3x (2) 7 (3) −3x+7-3x + 7 (4) 2f(x)+72f(x) + 7

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