Question

Question #a72ca

Answer 1

It is false.

Explanation:

For instance `|x|` is continuous, but does have derivate in `x=0`.

Additionally to the continuity, if have to guarantee that `f'(c^-)=f'(c^+)`

Answer 2

Another example is `f(x) = root(3)x`

Explanation:

`f(x) = root(3)x` is continuous at `0`, but `f'(x) = 1/(3root(3)(x^2))` is not defined at `0`.

It is possible to describe a function that is continuous everywhere, but differentiable nowhere. One example is the Weierstrass function.