it is not true. in fact c is a Critical Point:
consider the graph of this function:
but x=0 is not neither min nor max it is inflection point where the concavity of the graph will be diversed.
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.