Textbook Problem

The wind-chill index W in die perceived temperature when the actual temperature is T and the wind speed is v, so we can write W = f(T, v). The following table of values is an excerpt from Table 1 in Section 14.1.

(a) Estimate the values of f_T(−15, 30) and f_v(−15, 30). What are the practical interpretations of these values?

(b) In general, what can you say about the signs of ∂W/∂T and ∂W/∂v?

(c) What appears to be the value of the following limit?

$\underset{v\to \infty }{\lim }\frac{\partial W}{\partial v}$