Mathematics

Problem

The temperature (in

^{\circ}

C) in a city

t

hours after midnight is modelled by

T(t)=10+5\cos\!\bigl(\tfrac{\pi t}{12}\bigr)

for

6\le t\le18

. a. (i) Calculate the average rate of change of temperature between 6 a.m.

(t=6)

and 6 p.m.

(t=18)

. b. (ii) Obtain the expression for the instantaneous rate of change of temperature,

\dfrac{dT}{dt}

. c. (iii) Find all values of

t

in the open interval

(6,18)

at which the instantaneous rate equals the average rate found in part (i).