Let . Determine the value of such that the average rate of change of over the…

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

Problem

Let f(x)=x3f(x)=x^{3}. Determine the value of b (≠1)b\,(\neq 1) such that the average rate of change of ff over the interval [1,b][1,b] equals the instantaneous rate of change at x=1x=1. (a) 22 (b) −2-2 (c) −12-\dfrac12 (d) −1-1

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