A chemical engineer records the temperature T (in ∘C) of a reacting mixture every two minutes for ten minutes. A numerical estimate of the instantaneous rate of change T′(t) (in \(^\circ\!\text{C}\!\cdot\!\text{min}^{-1})$ at those same times is also provided.
Assume T is twice–differentiable on the interval 0≤t≤10 and that the numerical values in the table are accurate to within measurement error.
(a) Describe the behavior of T(t) on the interval 0≤t≤10 minutes. In your description, identify the subintervals on which T is increasing and those on which it is decreasing.
(b) Determine the time at which T attains a local extremum in the interval 0≤t≤10. State whether the extremum is a maximum or a minimum and justify your conclusion using the information in the table.
(c) Estimate the extreme temperature value and interpret its practical meaning in the context of the reaction.