Consider a box where the temperature inside is given by T (x, y, z) = 10xyz(2 x)(2 y)(4 z), with 0 x 2, 0 y 2, and 0 z 4. (a) Find the gradient of temperature, ~T . (b) Find the directional derivative of T at the point (1/2 , 1, 2) inside the box, in the direction of ~u = 1 + 1k. (c) If a fly is located at point (1/2, 1, 2) inside the box, in which direction (expressed as a vector) should it move in order to decrease the temperature as rapidly as possible? What is the rate of change of temperature that the fly experiences by moving in this direction?