3. Suppose the temperature in oF in a room is given by

T(x,y,z)=72+0.02z^2-0.03yx+0.04yz+0.1

wherex, y,andzare distances in feet from a lower corner of a rectangular room that is

10 x 10 x 10 feet. (xandyare horizontal distances from perpendicular walls, andzis the height above the floor, all in feet.)

a) Find the temperature of the room at the four corners of the room at the ceiling and at the geometric center of the room.

b) A bug at (0,6,9) flies in a straight line to the point (8,2,1). What rate of change of temperature will the bug experience at the time...

i) when it first begins flying and

ii) when it's half way to (8,2,1)

c) i) At it's final destination (8,2,1), which way could the bug fly from there to experience the greatest rate ofdecreaseof temperature?

ii) If the bug flew 1.25 feet in this direction (part i), what approximate change in temperature would occur?