For , calculate the average rate of change of at over each interval , , and . Using…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For f(x)=ln⁡xf(x)=\ln x, calculate the average rate of change of ff at x=3x=3 over each interval [3,3.2][3,3.2], [3,3.1][3,3.1], and [3,3.05][3,3.05]. Using the pattern you observe, state a numerical estimate (to four decimal places) for the instantaneous rate of change of ff at x=3x=3.

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