Hi there, just wanted to make a clarification before my final exam.(adsbygoogle = window.adsbygoogle || []).push({});

The second derivative test for partial derivatives (or at least part of it) states

if D = ∂^{2}f/∂x^{2}* ∂^{2}f/∂y^{2}- (∂^{2}f/∂x∂y)^{2}and (a,b) is a critical point of f, then

a) if D(a,b) > 0 and ∂^{2}f/∂x^{2}< 0, then there is a local max at (a,b)

b)if D(a,b) > 0 and ∂^{2}f/∂x^{2}> 0, then there is a local min at (a,b)

and the other two parts are irrelevant for my question. My question is, do I have tospecificallycheck that ∂^{2}f/∂x^{2}is positive or negative, or can I check that ∂^{2}f/∂y^{2}is positive or negative instead? i.e. does it really matter which one I check? Thank you in advance

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# Second Derivative Test for Partial Derivatives

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