Mathematics

Problem

Which function is continuous at

x=0

but NOT differentiable there? a)

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

h(x)=x^{2}

f(x)=|x|

k(x)=|x|^{3}

Intuitive explanation

The key is understanding that continuity and differentiability are different: a function can be unbroken at a point yet have a "sharp corner" or sudden change in slope there. Look for a function that passes through its point without jumping, but where the left and right derivatives don't match—or where the graph has a cusp or kink that prevents a single tangent line from existing.

Intuitive explanation

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