- #1

- 81

- 0

## Homework Statement

Find the maximum and minimum values of f(x,y) = x

^{5}y

^{3}on the circle defined by x

^{2}+ y

^{2}= 10. Do the same for the disc x

^{2}+ y

^{2}≤ 10.

## The Attempt at a Solution

for the first part, if I call the circle g(x,y) defined by x

^{2}+ y

^{2}= 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) = x

^{5}y

^{3}- λx

^{2}- λy

^{2}+ 10λ

OR

F(x,y,λ) = x

^{5}y

^{3}- λx

^{2}- λy

^{2}

(from there I can figure it out) I was just unclear as to how the constraint is handled.