Question

Suppose f(x) is continuous and differentiable. Must f'(x) be differentiable? Explain why or give an example why not.

Answer 1

Trying to think of an example of when it is false.
Try differentiating this function f twice:
f(x)=x^2 if x>=0 and -x^2 if x<0

Answer 2

@Satyaprakash2009rta

Answer 3

the answer is no

Answer 4

try f(x) = x^(4/3)
this is differentiable for all x (and therefore continuous)
but f ' (x) = 4/3 x^(1/3) is not differentiable for x = 0

Answer 5

@freckles can you help with his older question
prove that lim f(c*x) = lim f(x) as x -> 0 for both limits