Hi I just hit Lagrange in my calculus course and I like it alot because it makes life easier than testing out ever possible solution (like we did the chapter before)

Anyway I've been trying to use Lagrange on this problem:

Find min max values of:

f(x,y) = xy-y^2 on the disc x^2+y^2 =< 1

The "normal" (not used to it yet) approach would be going parametric equation

x=cos(t)

y=sin(t) -pi<=t=<pi

I don't see anything "normal" using parametric equations to solve a min-max problem, specially if asked to do so using Lagrange multipliers. However, is there any way possible to solve this cind of question using simply lagrange multipliers and clever reducing? I've not been able to reduce this problem in a way that would make things easier. If someone could show me how to think or how to attack a reducing problem like this i'd be very greatful. Use normal, usual, every-day Lagrange multipliers to solve the problem! Perhaps you still don't know that good what're Lagrange multipliers? They do NOT usually use parametric equations... Tonio
Also; Is Lagrange always the best viable option for solving problems like these? I really dont like using trigonometry in problems like these because I feel like i'd have an much easier time screwing up my calculations in the end. Also it would be nice to learn how to solve one problem in two ways.