$(1).$ Determine the direction towards which the temperature changes the most.

$(2).$ Determine the change in temperature with respect to time at $(x,y,z)=(0,0,0)$ and $(x,y,z)=(3km,3km,2km).$

$(3).$ Determine the change in temperature with respect to time according to someone traveling in a car

along $x$ at a speed of $100k\frac{m}{h}r$ and another at a speed of $150k\frac{m}{h}r$ after $6$ hours of driving. The

initial position of both cars is $(x,y,z)=(0,0,0),t=0.$