# How do you minimize and maximize #f(x,y)=x^2+y^(3/2)# constrained to #0<x+3y<2#?

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To minimize and maximize ( f(x, y) = x^2 + y^{3/2} ) constrained to ( 0 < x + 3y < 2 ), follow these steps:

- Find the critical points of ( f(x, y) ) by taking partial derivatives with respect to ( x ) and ( y ), then solving the system of equations ( \frac{\partial f}{\partial x} = 0 ) and ( \frac{\partial f}{\partial y} = 0 ).
- Check the critical points within the constraint region ( 0 < x + 3y < 2 ).
- Evaluate the function ( f(x, y) ) at the critical points and at the boundary points of the constraint region.
- Compare the values obtained to find the minimum and maximum values of ( f(x, y) ) within the constraint region.

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