Wind Chill When the air temperature is $20F,$ the rate of change of the wind chill temperature $t(F)$ is given by

$\frac{dt}{dw}=-4\mathrm{.}352w^{0\mathrm{.}84}$

where $w$ is wind speed in miles per hour.

a$.$ Will both the rate of change of wind chill temperature and wind chill temperature decrease as the windspeed increases? Explain.

Answer:

The wind chill temperature decreases because $\frac{dt}{dw}<mn>0</mn>$ for $w>0$

The rate increases because $\frac{d^{2}t}{d{w}^2}>0$ for $w>0.$