The temperature at each point (x, y, z) in a room is given by T(x, y, z) = xyz(1 - x)(2 - y)(3 - z), with 0 <= x <= 1, 0 <= y <= 2, and 0 <= z <= 3. If a mosquito is located at the point P(1/2, 1, 1),
a) In which direction should you fly to cool down as quickly as possible?
b) In which direction does the change of temperature become null?