Find the maximum and minimum outputs for f(x,y) = x^2y-x+y^2  on the set D= (x,y){ -2(less than or equal to)x(greater or equal to)2}, {-1(less than or equal to)y(greater than or equal to)2 } Solving using langrange multipliers, (y=x^2 is the graph )  Was wondering how to solve it completely & what langrage multipliers help us achieve, (my thinking is the max & min) of the function f without having to do it the other way where you find corner points, boundary points & critical points,  thank you :)

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