Multivariable Calculus Clarification Question
I just started to learn about extrema in calc III, and I just got to the second-partials 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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I don't think there is 1st derivative test for multi-variable functions
Do you think my method at the end there is necessarily wrong though? I can't think of a counterexample for it.
I guess you could try. If there was such method, it would have been written in calculus books already.