# A problem on local maxima and minima

I have been asked to find the local maxima/minima of the following two functions : $$i) f(x)=0.5(x_1+x_2+x_3)^2 + 0.5(x_1-x_3)^2 + x_1-2x_2+x_3$$ $$ii) f(x)=0.5(x_1+x_2+x_3)^2+0.5(x_1-2x_2+x_3)^2+3x_1+3x_3$$

Now it is straightforward. But, I am confused with the hints given as $[1 ~~ 1 ~~ 1]^T, [1 ~~ 0 ~~-1]^T, [1 ~~2 ~~-1]^T$ are orthogonal and $2[1 ~~ 1 ~~ 1]^T + [1 ~~ -2 ~~1]^T=[3 ~~ 0 ~~ 3]^T$

-
sorry, corrected that –  sosha Sep 29 '13 at 6:23