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anonymous
 one year ago
Multivariable Calculus Clarification Question
I just started to learn about extrema in calc III, and I just got to the secondpartials test. While I understand that this is akin to the second derivative test from calc I, is there no such thing as the first derivative test in multi? Like, can I use multiple sign charts for the components of the gradient to see whether or not it is an extrema or not?
anonymous
 one year ago
Multivariable Calculus Clarification Question I just started to learn about extrema in calc III, and I just got to the secondpartials test. While I understand that this is akin to the second derivative test from calc I, is there no such thing as the first derivative test in multi? Like, can I use multiple sign charts for the components of the gradient to see whether or not it is an extrema or not?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think there is 1st derivative test for multivariable functions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you think my method at the end there is necessarily wrong though? I can't think of a counterexample for it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I guess you could try. If there was such method, it would have been written in calculus books already.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I guess. I'll just keep on testing it on other practice questions until I hit a snag. If anyone can actual find/think of a case where it doesn't work, that'd be great though!
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