For the function

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

Problem

For the function f(x)=x3−6x2+9x+4f(x)=x^3-6x^2+9x+4, let AA denote the average rate of change of ff on the interval [1,3][1,3]. Which of the following correctly compares AA with the instantaneous rates of change f′(1)f'(1) and f′(3)f'(3)? (a) f′(1)<A<f′(3)f'(1) < A < f'(3) (b) A<f′(1) and A<f′(3)A < f'(1) \text{ and } A < f'(3) (c) A<f′(1) but A>f′(3)A < f'(1) \text{ but } A > f'(3) (d) A>f′(1) and A>f′(3)A > f'(1) \text{ and } A > f'(3)

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