- #1

aclotm81

- 2

- 0

## Homework Statement

By using the Lagrange multipliers find the extrema of the following function:

f(x,y)=x+y

subject to the constraints:

x

^{2}+y

^{2}+z

^{2}=1

y+z=1

**2. The attempt at a solution**

Using lambda = 1/(2x) I got x=y-z and y=1-z

plugging that into the first constraint, I got:

6y^2-6y+1=0 which makes y=0.5+-(3

^{1/2}/6)

I got the same thing when solving for z, which means x=0 and lambda = infinity, which doesn't make sense.