In previous section we have discussed that if a function is differentiable at a point, then it should be continous at that point and a discontinuous function cannot be differentiable. This fact is proved in following theorem

**Theorem:Â **If a function is differentiable at a point, it is necessarily continuous at that point.But the converse is not necessarily continuous true.

Or

f(x) is differentiable at x=cÂ f(x) is continuous at x=c

In order to prove that f(x) is continuous at x=c, it is sufficient to show that

Hence f(x) is continuous at x=c

**Converse:Â **The converse of above theorem is not necessarily true i.e., a function may be continuous may be continuous at a point but may not be differentiable at that point.

**For example: The function f(x) =|x| is continuous at x=0 but it is not differentiable at x=0, as shown in the figure.**

Which shows we have sharp edge at x=0 hence, not differentiable but continuous at x=0