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May 11th, 2014, 02:50 AM   #1
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critical points of function

hi all,

for function;
f(x,y)= ln(x+y) + x^2 - y - 64

I'm trying to find all critical points & determine whether there is a local max, local min, saddle point or none of these at each critical point.

thanks
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May 11th, 2014, 08:11 AM   #2
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Critical points are points where all the (partial)derivatives are equal to 0, and points where at least one of the derivatives is not defined.

The discriminant, to determine whether the point is maxima, minima or saddle point, is:

$\displaystyle \Delta = f_{xx}\,f_{yy} - f_{xy}^2$.

At which part of this you have difficulties?
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