Let . (a) Evaluate _ h 0^- f(0+h)-f(0) h and _ h 0^+ f(0+h)-f(0) h . (b) Based on…

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

Problem

Let f(x)=∣x∣f(x)=|x|. (a) Evaluate lim⁡h→0−f(0+h)−f(0)handlim⁡h→0+f(0+h)−f(0)h.\lim_{h\to 0^-}\frac{f(0+h)-f(0)}{h}\quad\text{and}\quad \lim_{h\to 0^+}\frac{f(0+h)-f(0)}{h}. (b) Based on these limits, determine whether ff is differentiable at x=0x=0.

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