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?
