If derivative doesn't exist at a point then this critical point cannot be a local minimum or maximum ? True or false?

Question

I think the question is false. Knowing that a critical point MUST be a point where the derivative is 0 or undefined, then of it can be a local min/local max. Please correct me if im wrong

Answer 1

F A L S E.  Relative extrema can only occur at critical points.

 

Incidentally, there's a bit of confusion in your comments e.g. "then of it can be..." is garbled.