- #1
SeannyBoi71
- 84
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Hi there, just wanted to make a clarification before my final exam.
The second derivative test for partial derivatives (or at least part of it) states
if D = ∂2f/∂x2 * ∂2f/∂y2 - (∂2f/∂x∂y)2 and (a,b) is a critical point of f, then
a) if D(a,b) > 0 and ∂2f/∂x2 < 0, then there is a local max at (a,b)
b)if D(a,b) > 0 and ∂2f/∂x2 > 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 to specifically check that ∂2f/∂x2 is positive or negative, or can I check that ∂2f/∂y2 is positive or negative instead? i.e. does it really matter which one I check? Thank you in advance
The second derivative test for partial derivatives (or at least part of it) states
if D = ∂2f/∂x2 * ∂2f/∂y2 - (∂2f/∂x∂y)2 and (a,b) is a critical point of f, then
a) if D(a,b) > 0 and ∂2f/∂x2 < 0, then there is a local max at (a,b)
b)if D(a,b) > 0 and ∂2f/∂x2 > 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 to specifically check that ∂2f/∂x2 is positive or negative, or can I check that ∂2f/∂y2 is positive or negative instead? i.e. does it really matter which one I check? Thank you in advance