How does one derive the second derivative test for three variables?(adsbygoogle = window.adsbygoogle || []).push({});

It's clear that

D(a,b) = fxx * fyy - (fxy)^2

AND

fxx(a,b)

Tells us almost all we need to know about local maxima and local minima for a function of 2 variables x and y, but how do I make sense of the second directional derivative of a function of 3 variables x,y,z to form the simple conclusions seen above????

I can easily take the second directional derivative of f(x,y) to derive the above.

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# Second derivative test and hessian matrix

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