1. Prove that for any p>1 and any x,y,z>=0,

( (x+y+z)/3 )^p <= (x^p + y^p + z^p)/3

2. Find the maximum and minimum of x^2 - y^2 + z^2 subject to x>=0, y>=0, z>=0, x+y+z<=10.

3. Find the maximum and minimum of x^2-y^2+z^2 subject to x^2+2y^2+z^2 =1 and x+2y+z=0.

Help appreciated.