The Heat Index chart in the next column shows the heat index, which combines the effects of temperature with humidity to give a measure of the apparent temperature, or how hot it feels to the body. For example, when the outside temperature is 90°F and the relative humidity is 40%, then the apparent temperature is approximately 93°F. Let I = ƒ(T, H) give the heat index, I, as a function of the temperature T (in degrees Fahrenheit) and the percent humidity H. Estimate the following.

(a) ƒ(90, 30) 

(b) ƒ(90, 75) 

(c) ƒ(80, 75)

Estimate the following by approximating the partial derivative using a value of h = 5 in the difference quotient.

(d) ƒ_T(90, 30) 

(e) ƒ_H(90, 30)
(f) ƒ_T(90, 75) 

(g) ƒ_H(90, 75)

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A G Q) E [r] I N Y E A R S [T Height (in.) 20 25 30 35 40 45 50 55 60 65 70 75 80 58" 1900 1850 1800 1750 1700 1650 1600 1550 1500 1450 1400 1350 1300 60" 2100 2050 2000 1950 1900 1850 1800 1750 1700 1650 1600 1550 1500 62" 2300 2250 2200 2150 2100 2050 2000 1950 1900 1850 1800 1750 1700 64" 2500 2450 2400 2350 2300 2250 2200 2150 2100 2050 2000 1950 1900 66" 2700 2650 2600 2550 2500 2450 2400 2350 2300 2250 2200 2150 2100 68" 2900 2850 2800 2750 2700 2650 2600 2550 2500 2450 2400 2350 2300 70" 3100 3050 3000 2950 2900 2850 2800 2750 2700 2650 2600 2550 2500 72" 3300 3250 3200 3150 3100 3050 3000 2950 2900 2850 2800 2750 2700 74" 3500 3450 3400 3350 3300 3250 3200 3150 3100 3050 3000 2950 2900