- #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)= x2y2z2
constraint: x2 + y2 + z2 = 1
Homework Equations
∇f = ∇g * λ
fx = gx * λ
fy = gy * λ
fz = gz * λ
The Attempt at a Solution
i can't solve for x, y, and lambda
i got:
for this one, fx = gx * λ ---> 2x*y2*z2=(2x)λ
for, fy = gy * λ ---> 2y*x2*z2=(2y)λ
fz = gz * λ ----> 2z*x2*y2=(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?