A room’s temperature (in degrees Celsius) hours after noon is modeled by T(t)=-0.2t^…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A room’s temperature (in degrees Celsius)

t

hours after noon is modeled by

T(t)=-0.2t^{3}+1.5t^{2}-3t+20, \quad 0\le t\le5.

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^{\circ}\text{C}

exactly once between noon and 5\,\text{P.M.}. (c) The temperature equals

18^{\circ}\text{C}

at least once between noon and 5\,\text{P.M.}. (d) No conclusion about the temperature equaling

18^{\circ}\text{C}

can be reached because

T

is not guaranteed to be continuous.