Question #a72ca

2 Answers
Feb 18, 2016

Answer:

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^+)#

Feb 19, 2016

Answer:

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.