So i was looking through past exams, and i came upon this question :
If the derivative does not exist at a point, then this critical point cannot be either a local maximum or a local minimum.
I think it is false.
Take for example, the function of f=absolute value of x. There is x=0. x=0 i assume is a critical point of the function due to the fact that the derivative doesn't exist at x=0.Please corrrect me if im wrong. I also understood that at x=0, there is a local minimum of the function .
So according to my understanding, the question is false. A critical point , where the derivative doesn't exists, can indeed be a local maximum or minimum .
correct?