(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lagrange Multipliers to find max/min values

**Physics Forums | Science Articles, Homework Help, Discussion**