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
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
it is not true. in fact c is a Critical Point:
consider the graph of this function:
$\displaystyle
f(x) = x^3
$
then
$\displaystyle
f^{\prime} (x) = 3x^2
$
and
$\displaystyle f^{\prime} (0) = 0$
but x=0 is not neither min nor max it is inflection point where the concavity of the graph will be diversed.