find maximum for a function on a ball I have a question thats giving me a hard time, can someone please help me out with it ?
I need to find maximun to the func:
$$
f(x) = 2-x+x^3+2y^3+3z^3 
$$
on the ball
$$
\{ (x,y,z) | x^2+y^2+z^2\leq1 \}
$$
what i have tried to do is this $$ (f_x,f_y,f_z)=0  $$ and then to check the H matrix. i got that $$ x= - \sqrt{\frac{1}{3}},   y=0,z=0 $$  but by wolfram-alpha i am wrong. could you help? thanks!

At first search for extremas in the interior. (With the normal way)
Than observe that for a maximum on the bound $x^2+y^2+z^2=1$ the derivative doesn't need to be zero, use lagrange multipliers here.
Look at the function 
$$g(x,y,z,\lambda)= 2-x+x^3+2y^3+3z^3+ \lambda (x^2+y^2+z^2-1)$$
and search find for a maximum for this function
