# LeGrange Multipliers Finding critical points of function

1. Oct 15, 2008

### Saladsamurai

1. The problem statement, all variables and given/known data

Find the critical points of $f(x,y)=x+y^2$ subject to the constraint $g(x)=x^2+y^2=1$

2. Relevant equations
$\nabla f=\lambda\nabla g$
$g(x,y)=1$

3. The attempt at a solution

$$f_x=1=2\lambda*x\Rightarrow x=\frac{1}{2\lambda}$$

$$f_y=2y=2\lambda*y\Rightarrow y(\lambda-1)=0\Rightarrow y=0 \\ or\\ \lambda=1$$

$$x^2+y^2=1$$

I am a little confused as to where I go from here?

2. Oct 16, 2008

### HallsofIvy

Staff Emeritus
You've done the hard part. If y= 0, then $\lambda$ doesn't matter: Find x from x2+ y2= 1. If $\lambda= 1$, then x= 1/2 and you can find y from x2+ y2= 1.

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