(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

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# Lagrange multipliers with two constraints

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