- #1
maks4
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- 0
Homework Statement
Using Lagrange Multipliers, we are to find the maximum and minimum values of f(x,y) subject to the given constraint
Homework Equations
f(x,y,z) = x^2 - 2y + 2z^2, constraint: x^2 + y^2 + z^2 = 1
The Attempt at a Solution
grad f = lambda*grad g
(2x, -2, 4z) = lambda(2x, 2y, 2z)
therefore: 2x = lambda2x
-2 = lambda2y
4z = lambda2z
Now i can see how x and z can both equal 0, and how lambda can equal 1, and how y eventually equals -1 and f(0,-1,0)=2, yet in the solutions there is another part to it where it says
OR, Lambda = 2, y = -1/2, x = 0, z= +- sqrt(3)/2. <---i do not have any idea how these values came to be, no idea at all. Any help would be appreciated, thanks.