For a differentiable function

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

Problem

For a differentiable function ff, which of the following expressions gives the average rate of change of ff on the interval [a,a+h][a, a+h] where h≠0h\neq 0? (a) lim⁡h→0f(a+h)−f(a)h\displaystyle \lim_{h\to 0}\frac{f(a+h)-f(a)}{h} (b) f(a+h)−f(a)h\displaystyle \frac{f(a+h)-f(a)}{h} (c) f(a+h)−f(a)a+h\displaystyle \frac{f(a+h)-f(a)}{a+h} (d) f(a+h)−f(a−h)2h\displaystyle \frac{f(a+h)-f(a-h)}{2h}

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