1. Suppose that the outdoor temperature (in Fahrenheit) on a particular day was approximated by the function
T(t) = 50 + 14sin[(pi(t))/12]
Where t is time in hours after 9 AM.
a) find the max (Tmax) and min (Tmin) temperature, And the average temperature:
Tav = 1/12 ∫(0 —> 12) T(t)dt on that day during the period between 9 AM and 9 PM.
B) show that Tav is not equal to (Tmin + Tmax)/2
C) show that T is not given by the above formula, but rather T(t) is a linear function of t, then Tav= (Tmin+Tmax)/2
(use an integral to explain)