Livinia, the housefly, finds herself caught in the oven at the point (0, 0, 1). The temp...

Livinia, the housefly, finds herself caught in the oven at the point (0, 0, 1). The temperature at points in the oven is given by the function

where the units are in degrees Celsius. (a) If Livinia begins to move toward the point (2, 3, 1), at what rate (in deg/cm) does she find the temperature changing?

(b) In what direction should she move in order to cool off as rapidly as possible?

(c) Suppose that Livinia can fly at a speed of 3 cm/sec. If she moves in the direction of part (b), at what (instantaneous) rate (in deg/sec) will she find the temperature to be changing?