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**Lagrange Multipliers Question???**

## Homework Statement

Find the minimum and maximum values of the function subject to the given constraint.

f (x,y,z) = x^2 - y - z, x^2 - y^2 +z = 0

## The Attempt at a Solution

Okay this is what I did:

Gradient f = <2x,-1,-1> Gradient g = <2x,-2y,1>

Gradient f = (Lambda) Gradient g

<2x,-1,-1> = L <2x,-2y,1>

2x = L(2x) L=1

-1=-L(2y)

-1=L(1)

by this Lambda = 1 and -1? How can this be, am I doing something wrong? Thanks for the help.