Mathematics

Problem

Which function is continuous on

\mathbb{R}

but fails to be differentiable at

x=2

specifically because the tangent line is vertical at that point? a)

g(x)=|x-2|

g(x)=\dfrac{1}{x-2}

g(x)=(x-2)^{1/3}

g(x)=(x-2)^{2/3}