When we are finding critical points (with the first or 2nd derivative), it has been told to us that it is when we set the derivative (1st or 2nd depending on the case) to 0. Whenever the derivative =0 or is undefined, is a critical point. However, I've noticed a pattern that when the point is undefined starting from the original function itself, there is no use in even considering it a critical value since it doesn't help. Is this true?

Question

When we are finding critical points (with the first or 2nd derivative), it has been told to us that it is when we set the derivative (1st or 2nd depending on the case) to 0.  Whenever the derivative =0 or is undefined, is a critical point.  However, I've noticed a pattern that when the point is undefined starting from the original function itself, there is no use in even considering it a critical value since it doesn't help.  Is this true?

abb0t · Answer

Not all functions will have critical points.

anonymous · Answer

I'm talking about a point in general.

anonymous · Answer

This is another tool in your tool box of studying functions, eg, in pre-cal one studies end behavior, etc, of functions. As you go on in calculus, you get questions like is this point a max, min, or neither (saddle point).

anonymous · Answer

Hi, I think I resolved my own question.  A critical value can be when the function exists, but the derivative doesn't (how could I forget!).