Suppose that the temperature at points inside a room is given by a differentiable function T (x, y, z). Livinia, the housefly (who is recovering from a head cold), is in the room and desires to warmup as rapidly as possible.
(a) Show that Livinia’s path x(t) must be a flow line of k∇T , where k is a positive constant.
(b) If T (x, y, z) = x2 − 2y2 + 3z2 and Livinia is initially at the point (2, 3,−1), describe her path explicitly.
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