The temperature T at a location in the Northern Hemisphere depends on the longitude x, latitude y, and time t so we can write T=f(x,y,z); time is measured in hours from the beginning of January.
Honolulu has longitude 158 degrees W, and latitude 21 degrees N. Suppose that at 9:00 AM on January 1, the wind is blowing hot air to the northeast, so the air to the west and south is warm and the air to the north and east is cooler. Would you expect fx(158, 121,9), fy(158, 121,9), and ft(158, 121,9) to be positive or negative? Explain.
dT/dx = change in temperature as longitude varies
dT/dy = change in temperature as latitude varies
dT/dt = change in temperature as time varies
The Attempt at a Solution
As longitude varies, the temperature in the north would get cooler, so would it be a negative partial derivative?
I'm not sure how to approach this.