Mathematics

Problem

The temperature

T

(in

^{\circ}\!\text{C}

) of a liquid cooling in a room is modelled by

T(t)=3t^{2}-12t+5,

where

t

is the time in minutes. a. (i) Explain the physical meaning of the derivative

T'(t)

in this context. b. (ii) Calculate

T'(2)

and interpret its sign. c. (iii) Compute the average rate of change of temperature between

t=2\,\text{min}

and

t=3\,\text{min}

, and contrast it with the instantaneous rate found in part (ii).