(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

3. 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.

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# Homework Help: Lagrange multiplier question

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