At 6:00 A.M. the outside temperature was , and at noon it was . The temperature is…
MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
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.