Let be differentiable at

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

Problem

Let ff be differentiable at x=ax=a, and let h>0h>0 be small. Which of the following expressions provides a symmetric numerical approximation of f′(a)f'(a)? (a) f(a+h)−f(a−h)h\dfrac{f(a+h)-f(a-h)}{h} (b) f(a+h)−2f(a)+f(a−h)h2\dfrac{f(a+h)-2f(a)+f(a-h)}{h^{2}} (c) f(a+h)−f(a−h)2h\dfrac{f(a+h)-f(a-h)}{2h} (d) f(a+h)−f(a)h\dfrac{f(a+h)-f(a)}{h}

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