   Chapter 14.3, Problem 1E

Chapter
Section
Textbook Problem

The temperature T (in °C) at a location in the Northern Hemi-sphere 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 fx(158, 21, 9), fy(158, 21, 9), and ft(158, 21, 9) to be positive or negative? Explain.

(a)

To determine

To find: The meaning of the partial derivatives Tx,Ty and Tt .

Explanation

Given:

The function is T=f(x,y,t) where T is temperature (in °C ), x is longitude, y is latitude and t is time.

Solution:

The partial derivative Tx represents the rate of change of the temperature T with respect to the longitudex and keeping the latitude y and timet as constant

(b)

To determine

To explain: The sign of fx(158,21,9),fy(158,21,9) and ft(158,21,9) .

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