At 6:00 A.M. the outside temperature was 48∘F, and at noon it was 68∘F. The temperature T(t) is modeled by a function that is continuous for 6≤t≤12, where t is measured in hours after midnight.
Which of the following statements must be true?
a) The temperature increased at a constant rate over the interval from 6:00 A.M. to noon.
b) There was a time between 6:00 A.M. and noon when the temperature was exactly 60∘F.
c) There existed a time between 6:00 A.M. and noon when the instantaneous rate of change of the temperature was exactly 3.33∘F per hour.
d) The highest temperature on the interval from 6:00 A.M. to noon occurred exactly at noon.