Math Help - derivative relation query

1. derivative relation query

Question is if f(x) is a differentiable function. If f'(c)=0 then f(x) has a local maximum or minimum at x=c. True of False?

I would have thought this was true but answer in text states otherwise.

Could someone clarify and explain please.
Thanks

2. it is not true. in fact c is a Critical Point:

consider the graph of this function:

$
f(x) = x^3
$

then

$
f^{\prime} (x) = 3x^2
$

and

$f^{\prime} (0) = 0$

but x=0 is not neither min nor max it is inflection point where the concavity of the graph will be diversed.

3. Let $f(x)=x^3$. What is the derivative of f evaluated at x=0? What happens to f at x=0?

4. Thanks guys, makes perfect sense. Think I must be a little