# How do you minimize and maximize #f(x,y)=x^2y-xy# constrained to #3<x+y<5#?

There are local maxima at

and local minima at

Introducing the so called slack variables

Find local minima, maxima of

subject to

The lagrangian is

The determination of stationary points is done solving for

or

Solving we get

The first and second points are at the boundaries of

Their qualification must be done with

Attached a figure with a contour mapping with the points found.

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To minimize and maximize ( f(x,y) = x^2y - xy ) constrained to ( 3 < x + y < 5 ), you need to first find the critical points of the function within the constraint. Then, evaluate the function at these critical points as well as at the boundary points of the constraint to determine the minimum and maximum values.

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