A calculator’s numeric derivative command returns for

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

Problem

A calculator’s numeric derivative command returns f′(0)≈−1.0×10−7f'(0)\approx-1.0\times10^{-7} for f(x)=x3sin⁡xf(x)=x^{3}\sin x. Using h=0.001h=0.001, compute the symmetric difference quotient f(h)−f(−h)2h\dfrac{f(h)-f(-h)}{2h} (give eight decimal places) and state whether the calculator’s result is consistent with your quotient.

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