AP

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let f(x)=3x3−5x+7f(x)=3x^{3}-5x+7. (i) Write an expression for the average rate of change of ff on the interval [2,2+h][2,2+h], where h≠0h\neq0. (ii) Hence find the instantaneous rate of change of ff at x=2x=2. (iii) Calculate the numerical value obtained in part (ii).

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