Consider a particle that moves in

={(, , ):² +2² +2² 4}, and is subject to the force field given by (,,)=(1,2,2).

(a) Show that is conservative and find a potential for it, that is, a function:³ with=.

(b) Use (a) to compute the work(,,) done by to move our particle from(1, 1, 0)to a point(,,)in.

(c) Determine the maximum and minimum values of(,,) in, listing all points at which those values occur.