A laboratory technician heats a liquid whose temperature (in degrees Celsius) after…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A laboratory technician heats a liquid whose temperature (in degrees Celsius) after t minutes is modeled by
T(t)=3t2+mt+20.
The technician wants the average rate of change of the temperature over the first four minutes to be exactly 26∘C/min.
(1) Derive an expression, in terms of m, for the average rate of change of T over the interval [0,4]. State your result in degrees Celsius per minute.
(2) Determine the value of m that yields the desired average rate of change.
(3) Interpret the meaning of your value of m in the context of the heating process.