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

Use Lagrange multipliers to find the max and min values of the function subject to the given constraints:

f(x,y,z)= x^{2}y^{2}z^{2}

constraint: x^{2}+ y^{2}+ z^{2}= 1

2. Relevant equations

∇f = ∇g * λ

f_{x}= g_{x}* λ

f_{y}= g_{y}* λ

f_{z}= g_{z}* λ

3. The attempt at a solution

i cant solve for x, y, and lambda

i got:

for this one, f_{x}= g_{x}* λ ---> 2x*y^{2}*z^{2}=(2x)λ

for, f_{y}= g_{y}* λ ---> 2y*x^{2}*z^{2}=(2y)λ

f_{z}= g_{z}* λ ----> 2z*x^{2}*y^{2}=(2z)λ

i tried setting them all equal to lambda, and ended up getting that x=y=z=1 but when you add that into g(x,y,z).... that equals >1 ? im confused with getting the x,y,z, and lambda values. help?

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# Homework Help: Lagrange Multipliers to find max/min values

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