The highest recorded temperature in the state of Alaska was 100 F and occurred on June 27, 1915, at Fort Yukon. The heat index is the apparent temperature of the air at a given temperature and humidity level. If x denotes the relative humidity (in percent), then the heat index (in degrees Fahrenheit) for an air temperature of 100 F can be approximated by the function
f (x) = 0.009x2 + 0.139x + 91.875
(a) At what rate is the heat index changing when the humidity is 50%?
(b) Write a sentence that explains the meaning of your answer in part (a).