Which function is continuous on but fails to be differentiable at specifically…

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

Problem

Which function is continuous on R\mathbb{R} but fails to be differentiable at x=2x=2 specifically because the tangent line is vertical at that point? (a) g(x)=∣x−2∣g(x)=|x-2| (b) g(x)=1x−2g(x)=\dfrac{1}{x-2} (c) g(x)=(x−2)1/3g(x)=(x-2)^{1/3} (d) g(x)=(x−2)2/3g(x)=(x-2)^{2/3}

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