Would all be helping me out here alot

Find the local maxima and minima of the following function:

$\displaystyle f(x_1,x_2,x_3)=x_1 + 2x_2 + x_3$

Subject to the constraints:

$\displaystyle x_1^2+x_2^2+x_3^2=2$ and, $\displaystyle x_1^2+(x_2-1)^2+x_3^2=3$

The answers I got were:

$\displaystyle (x_1,x_2,x_3)=(1,0,1)$ with $\displaystyle \lambda_1=-\frac{3}{2}, \lambda_2=1$ ... This gives a local maximum.

Also...

$\displaystyle (x_1,x_2,x_3)=(-1,0,-1)$ with $\displaystyle \lambda_1=-\frac{1}{2}, \lambda_2=1$ ... This gives a local minimum.

I hope these are right. If I have made an error, and you want my working just reply... thanks!!