RE: How to calculate the relative extrema of a cubic function by applying the criterion of the first derivative?
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Good work but you forgot the importance of checking the second derivative. It has to be non zero for your first derivate zeros to be the max/min of the original function.
They also tell you (if they are non zero) whether your original has a minimum or maximum. If the second derivative is positive it means your first derivative is transfering from negative to positive at its zero and the original function first had a decline in values and after that rises in values which means it's a minimum. Vice versa for the maximum.
Should both derivatives be zero you have a saddle point in your original function.
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I will take into account your considerations for a future publication, since the objective of this one was to use the criterion of the first derivative. I will take into account the criterion of the second derivative for my next publication.
Greetings, I hope to continue reading your comments in my next posts.
My comment was trigger by exactly that thought. As I said, it can be misleading if the second is zero as well. In that case you might think you found an extreme while you are actually hitting on a saddle. While at it I added the discussion point about the difference between max and min.
Sorry if that was too exhausting, once I get triggered by math I cannot resist :-P
!BBH
Hello friend, of course I understand you, we are in contact, thanks for encouraging a good debate.
@carlos84! @hannes-stoffel likes your content! so I just sent 1 BBH to your account on behalf of @hannes-stoffel. (2/50)
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