- #1

arl146

- 343

- 1

## Homework Statement

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

## Homework Equations

∇f = ∇g * λ

f

_{x}= g

_{x}* λ

f

_{y}= g

_{y}* λ

f

_{z}= g

_{z}* λ

## The Attempt at a Solution

i can't 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 ? I am confused with getting the x,y,z, and lambda values. help?