If a function satisfies

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

Problem

If a function ff satisfies lim⁡x→0−f(x)=lim⁡x→0+f(x)=f(0)\displaystyle \lim_{x\to0^-}f(x)=\lim_{x\to0^+}f(x)=f(0), but lim⁡h→0−f(0+h)−f(0)h≠lim⁡h→0+f(0+h)−f(0)h\displaystyle \lim_{h\to0^-}\frac{f(0+h)-f(0)}{h}\neq\lim_{h\to0^+}\frac{f(0+h)-f(0)}{h}, then at x=0x=0 the function is (a) continuous and differentiable (b) continuous but not differentiable (c) discontinuous but differentiable (d) discontinuous and not differentiable

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