Consider a particle that moves in M = {(x, y, z) : 2×2 + 242 + 22 < 4}, and is subject to the force field given by F(x, y, z) = (2x, -2z, -2y). (a) Show that F is conservative and find a potential for it, that is, a function f : R3 -> R with Vf = F.
Consider a particle that moves in
M = {(x, y, z) : 2×2 + 242 + 22 < 4},
and is subject to the force field given by
F(x, y, z) = (2x, -2z, -2y).
(a) Show that F is conservative and find a potential for it, that is, a function f : R3 -> R with Vf = F.
(b) Use (a) to compute the work W(x, y, z) done by F to move our particle from (0, 1, 1) to a point (x, y, z) in M.
(c) Determine the maximum and minimum values of W(x, y, z) in M, listing all points at which those values occur.
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