# Extreme values

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1.)f(x,y)= 5 - 3x + 4y, D is the closed triangular region with vertices (0,0), (4,0), and (4,5)

2.)f(x,y)= x^2 + 2xy + 3y^2, D is the closed triangular region with vertices (-1,1), (2,1), and (-1,-2)

3.)f(x,y)= 1 + xy - x - y, D is the region bounded by the parabola y=x^2 and the line y=4

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#### Solution Preview

1. , is a closed triangular region with vertices , and . To find the maximum and the minimum of , we calculate the followings.

, . So does not have critical points.

, ,

Thus the maximum value of is ; the minimum value of is .

2. , is a closed triangular region with vertices , and . Then ...

#### Solution Summary

This provides examples of finding extreme values of a function on a set.

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