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?