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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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abb0tBest ResponseYou've already chosen the best response.0
Not all functions will have critical points.
 one year ago

SujayBest ResponseYou've already chosen the best response.0
I'm talking about a point in general.
 one year ago

chaguanasBest ResponseYou've already chosen the best response.0
This is another tool in your tool box of studying functions, eg, in precal 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).
 one year ago

SujayBest ResponseYou've already chosen the best response.0
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!).
 one year ago
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