What is the minimum and maximum?

Question

Find the minimum and maximum values of the function f(x,y) = (x^2)y + x + y subject to the constraint xy = 9.

minimum: ?

maximum: ?

Answer 1

Because f(x,y) is constrained to xy = 9, you can substitute y= x/9 into the f(x,y) in order to get 10x+9/x.

You can now take the derivative, set it equal to zero and find the critical points x=sqrt(.9) I'll leave it to you to determine min/max. You might try plotting y = 10x + 9/x for insight.