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

T(x,y,z) = 10 (xe^{(-y2)} + ze^{(-x2)})

where the units are in degrees celsius.

(i.)so if livinia begins to move towards the point (2,3,1) at what rate in deg/cm does she find the temp. changing?

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

(iii.)suppose that livinia can fly at a speed of the square root of 2 (cm/sec.) if she moves in the direction of part (ii) at what rate will she find the temp. to be changing?