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March 18th, 2009, 12:53 PM   #1
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Quick Second Partial Derivative Test Question

I understand that when the discriminant of a function defined as is less than zero at point (a,b) then the function has a saddle point at (a,b) and if the discriminant is greater than zero at (a,b) there exists a local extrema at point (a,b) (D=0 is inconclusive). Also if there is a local extrema then:

there exists a local minimum at (a,b)
there exists a local maximum at (a,b)

However what about the case that D>0 at (a,b) indicating that there is a local extrema, but ? This can't be a saddle point can it? Or does the test fail?
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March 18th, 2009, 11:38 PM   #2
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Re: Quick Second Partial Derivative Test Question

In that case look at instead.

Also: the singular is extremum, the plural is extrema.
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March 19th, 2009, 07:51 PM   #3
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Re: Quick Second Partial Derivative Test Question

Ahh ok thank you. Is there any particular reason we choose to evaluate first rather than ?
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March 19th, 2009, 09:21 PM   #4
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Re: Quick Second Partial Derivative Test Question

No. You can check any directional derivative.
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