Hi my name is Tara Doucet at I am taking calculus at Nipissing University.

My question is Maximize Q=xy^2 (y is to the exponent 2) where x and y are positive integers such that x + y^2 ( y is to the exponent 2)=4

Hope you get this and I hope you can help me out.


What follows is the reply that I sent to Tara but it doesn't produce the required solution. Penny has the correct solution.


Hi Tara,

The expression that you want to maximize, Q = x y 2, is a function of two variables, x and y. You must find a way to express Q as a function of one variable to apply the calculus techniques that you have learned. The necessary information to express Q as a function of one variable is the restriction that x + y 2 = 4. I would rewrite this equation y 2 = 4 - x and substitute into Q to get Q = x(4 - x). Now maximize Q.

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