The Wind-chill index is a function of temperature and wind speed and is represented as .

(a)

Estimate .

.

Assume values depending on Table 1 in section 14.1.

Let .

Observe the table: and .

For , .

Let .

Observe the table: and .

For , .

Therefore, the average of the two values is .

.

For a temperature of and constant wind speed of , the wind-chill index rises by for each degree the temperature increases.

Estimate .

.

Assume values depending on Table 1 in section 14.1.

Let .

Observe the table: and .

For , .

Let .

Observe the table: and .

For , .

Therefore, the average of the two values is .

.

For a constant temperature of and wind speed of , the wind-chill index decreases by for each rise in the wind speed.

(b)

Observe the values of and :

is positive because as temperatures increases, the change in wind chill index also increases.

is negative because as wind speed increases, the change in wind chill index decreases.

(c)

is negative because as wind speed increases, the change in wind chill index decreases.

Hence it is assumed that tends to zero as .

Therefore, .

(a)

.

For a temperature of and constant wind speed of , the wind-chill index rises by for each degree the temperature increases.

.

For a constant temperature of and wind speed of , the wind-chill index decreases by for each rise in the wind speed.

(b) is positive and is negative.

(c) .