Chapter 2, Problem 84RE

Suppose on a certain day the low temperature was 32° at midnight, the high temperature was 65° at noon, and then the temperature dropped to 32° the following midnight. Prove there were two times during that day, which were 12 hours apart, when the temperatures were equal (Hint: Let T(t) equal the temperature t hours after midnight and examine the function $f\left(t\right)=T\left(t\right)-T\left(t+12\right)$, for $0\le t\le 12$.)