Mathematics

Problem

The temperature

T

(in

^{\circ}\!\mathrm{C}

) inside a metal rod at time

t

minutes is given by

T(t)=4t^{2}-2t+3\sin t

. a. (a) Determine

T\bigl(\tfrac{\pi}{6}\bigr)

and

T\bigl(\tfrac{\pi}{3}\bigr)

. b. (b) Find the average rate of change of temperature over the interval

\bigl[\tfrac{\pi}{6},\tfrac{\pi}{3}\bigr]

and state appropriate units. c. (c) Decide whether the temperature is rising faster or slower than

0.5\,^{\circ}\!\mathrm{C}

per minute on this interval, justifying your answer using the value obtained in part (b).