MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A cup of tea is left to cool on a counter. The temperature T of the tea, measured in degrees Celsius, is a differentiable function of time t, measured in minutes after the tea is poured. A laboratory thermometer records the following information at t=4:
• T(4)=68
• T′(4)=−3.2
Assume that T is decreasing and concave up for 0≤t≤10.
(a) Interpret the numerical value T′(4)=−3.2 in the context of the problem. State appropriate units.
(b) Explain what the negative sign of T′(4) indicates about the behavior of the tea’s temperature at t=4 minutes.