# Thread: If f ' (a) = 0, is always true that...

1. ## If f ' (a) = 0, is always true that...

If f'(a)=0, then there will always be a local extreme at x=a. Is this statement true or false. Explain and if it is false give a counter example.
I say this is true because for f'(a)=0 that means that on f(x), x=a represent a point where mtangent=0 , representing a local extreme.
Am I correct?

Thanks!

2. ## Re: If f ' (a) = 0, is always true that...

Originally Posted by sakonpure6
I say this is true because for f'(a)=0 that means that on f(x), x=a represent a point where mtangent=0 , representing a local extreme.
You really need to carefully think about the function $f(x)=x^3$ at $x=0$.