Give an example of a function which is continuous but not differentiable at a point.

Question

Philoid · Accepted Answer

Consider the function f(x) = |x| where

This function is continuous at x = 0 but not differentiable at x = 0.

LHL at x =0,

RHL at x =0,

And f(0)=0

Hence, f(x) is continuous at x =0.

LHD at x =0,

RHD at x =0,

∵ LHD ≠RHD

∴ f(x) is not differentiable at x =0.