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# How do you classify the stationary points of a surface f(x,y)=z watch

1. Say you had the following function:

I know that the stationary points occur at the point where so the stationary points for this function would be and . How would you classify these points?

I know it has something to do with comparing and .

Posted from TSR Mobile
2. (Original post by Brian Moser)
Say you had the following function:

I know that the stationary points occur at the point where so the stationary points for this function would be and . How would you classify these points?

I know it has something to do with comparing and .

Posted from TSR Mobile
If (a,b) is a stationary point then it is a local maximum if f(a+h,b+k)<f(a,b) for all sufficiently small h,k (not both zero)
It is alocal minimum if f(a+h,b+k)>f(a,b) mfor all sufficiently small h,k (not both zero)
It is a saddle point if f(a+h,b+k)<f(a,b) for some values of h.k but >f(a,b) for other values
or lkook at
www3.ul.ie/~mlc/support/Loughborough%20website/chap18/18_3.pdf

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Updated: January 7, 2015
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