A room’s temperature (in degrees Celsius) t hours after noon is modeled by
T(t)=−0.2t3+1.5t2−3t+20,0≤t≤5.
Which of the following is most strongly supported by this model?
a) There is some time when T(t)=18 and T′(t)=0.
b) The temperature equals 18∘C exactly once between noon and 5\,\text{P.M.}.
c) The temperature equals 18∘C at least once between noon and 5\,\text{P.M.}.
d) No conclusion about the temperature equaling 18∘C can be reached because T is not guaranteed to be continuous.