Find the maximum and minimum values of f(x,y) = x5y3 on the circle defined by x2 + y2 = 10. Do the same for the disc x2 + y2 ≤ 10.
The Attempt at a Solution
for the first part, if I call the circle g(x,y) defined by x2 + y2 = 10
I need to now define some F(x,y,λ) = f(x,y) - λg(x,y) and find the critical points of this, i.e.: where Fx', Fy', and Fλ' = 0. I was wondering if I should include the constant (10) in the function λg, or does it matter at all? i.e.:
F(x,y,λ) = x5y3 - λx2 - λy2 + 10λ
F(x,y,λ) = x5y3 - λx2 - λy2
(from there I can figure it out) I was just unclear as to how the constraint is handled.