Chapter 4.10, Problem 10P

The temperature at a point $(x,y,z)$ in the ball $x^2+y^2+z^2\le 1$ is given by $T=y^2+xz$.

Find the largest and smallest values which $T$ takes

(a) on the circle $y=0,x^2+z^2=1$, (b) on the surface $x^2+y^2+z^2=1$, (c) in the whole ball.