The temperature (in degrees Celsius) of a cup of coffee cooling on a countertop is…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
The temperature (in degrees Celsius) of a cup of coffee cooling on a countertop is modeled by the differentiable function
T(t)=15+10sin(12πt),
where t is measured in hours after midnight. Numerical answers should be rounded to three decimal places.
(a) Approximate T′(8.5) and include correct units with your answer.
(b) Interpret the value found in part (a) in the context of the cooling coffee. Clearly explain what the sign and magnitude of T′(8.5) convey about the temperature at 8:30 a.m.