# Let f(x, y) = 1 + xy - 2x + y and let D be the triangular region with vertices (-2, 1),...

## Question:

Let {eq}f(x, y) = 1 + xy - 2x + y {/eq} and let {eq}D {/eq} be the triangular region with vertices (-2, 1), (-2, 5), and (2, 1). Find the absolute maximum and minimum values of {eq}f {/eq} on {eq}D {/eq}.

## Absolute Maximum And Minimum value Of A Function

Using partial order derivative test we can find the absolute maximum or minimum value

of a function {eq}f(x,y) {/eq}.

First we find the critical points using first order partial derivative then

from second order partial derivative we check the value of the discriminant {eq}D=f_{xx}f_{yy}-(f_{xy})^{2} {/eq}

at these critical points.If {eq}D<0 {/eq} then it gives a saddle point and if {eq}D>0 {/eq} then it gives either a maximum or a minimum point.

## Answer and Explanation:

Given function is {eq}f(x,y)=1+xy-2x+y {/eq}

Now,the first order partial derivatives are {eq}\\\\f_{x}=y-2 \\\\f_{y}=x+1 {/eq}

Equating them to...

See full answer below.

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