Wind chill temperature (or index) is the perceived air temperature felt by exposed skin due to a cold wind. It is calculated by the formula W = 35.74 + 0.6125T − 35.75v^0.16 + 0.4275T v^0.16, Where T is temperature in Fahrenheit (T ≤ 40) and v is wind speed in miles per hour. (a) Show that ∂W/∂T 0 for all T , assuming v ≥ 0. Explain, in physical terms, why this should be so. (b) Show that ∂W/∂V

Question

Wind chill temperature (or index) is the perceived air temperature felt by exposed skin due to a cold wind. It is calculated by the formula 
W = 35.74 + 0.6125T − 35.75v^0.16 + 0.4275T v^0.16,
Where T is temperature in Fahrenheit (T ≤ 40) and v is wind speed in miles per hour.

(a) Show that ∂W/∂T > 0 for all T , assuming v ≥ 0. Explain, in physical terms, why this should be so.
(b) Show that ∂W/∂V < 0 for all v, assuming T ≤ 40. Explain, in physical terms, why this should be so.
(c) Find the linearization of W at 20◦F and 15 mph.