The following table shows the wind chill C(T,w) (in °F ) as a function of the air temperature T (in °F ) and the wind speed w (in miles per hour)

according to the current National Weather Service model.

There are three ways to estimate a partial derivative from a table of values, the forward difference quotient (for example,

fx(a,b)~~f(a+h,b)-f(a,b)h with h>0 ), the backward difference quotient (for example, fx(a,b)~~f(a,b)-f(a-h,b)h with h>0 ), and the

symmetric difference quotient (for example, fx(a,b)~~f(a+h,b)-f(a-h,b)2h with h>0 ). The symmetric difference quotient is just the average

of the forward and backward difference quotients.

The forward difference quotient approximation to CT(30,15) is

°F°F. The backward difference quotient approximation to

CT(30,15) is

°F°F. The symmetric difference quotient approximation to CT(30,15) is

°F°F.

The forward difference quotient approximation to Cw(30,15) is

°Fmph. The backward difference quotient approximation to

Cw(30,15) is

°Fmph. The symmetric difference quotient approximation to Cw(30,15) is

°Fmph.

The National Weather Service has also provided an empirical formula for approximating the wind chill. It states that

C(T,w)~~35.74+0.6215T+w0.16(-35.75+0.4275T)

Based on this formula, CT(30,15)~~

°F°F and Cw(30,15)~~

°Fmph.