The temperature T (in °C) 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, t). Let’s measure time in hours from the beginning of January.

(a) What are the meanings of the partial derivatives ∂T/∂x, ∂T/∂y, and ∂T/∂t?

(b) Honolulu has longitude 158°W and latitude 21°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 f_x(158, 21, 9), f_y(158, 21, 9), and f_t(158, 21, 9) to be positive or negative? Explain.