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I know how to find the absolute maximum and minimum values of a function in one variable. It can be found by differentiating the function and sitting it to zero and then solving for the unknown. But i would like to know how to find the maximum value of a function in 2 variable.

user258250
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  • See http://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/min_max/min_max.html or else. – georg Sep 10 '15 at 15:14

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This stuff is all over Wikipedia and Google, but well...

This is done by the Second partial derivative test.

First find the point(s) $p_n$ where all first derivatives of the function are $0$.

Let $f_{ab}$ represent a function with it's derivative first taken to the variable a and then to the variable b, with the second taken constant. Then for your point $p_n$ calculate:

$$D=f_{11}f_{22}-f_{21}f_{12}$$

Which is also the determinant of the Hessian Matrix.

If $D>0$ you have a minimum or maximum. If $f_{11}<0$ it's a maximum, otherwise its a minimum.

If $D<0$ it's a saddle point, if $D=0$ then the test is inconclusive.

Feyre
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