MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
During a chemistry experiment, the temperature T (in °C) of a solution is a differentiable function of time t (in minutes). It is known that T′(t)<0 for 0<t<6, T′(6)=0, and T′(t)>0 for 6<t<12. Which statement is most accurate about the behavior of T at t=6 minutes?
(a) The temperature attains a local maximum at t=6 minutes.
(b) The temperature attains a local minimum at t=6 minutes.
(c) The temperature has an inflection point at t=6 minutes but neither a maximum nor minimum.
(d) The information provided is insufficient to determine the behavior of T at t=6 minutes because T′′(6) is unknown.