The temperature (in °C) of a city’s water reservoir is recorded as a differentiable…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The temperature

T

(in °C) of a city’s water reservoir is recorded as a differentiable function of time

t

(in hours). A calculation gives

T'(10)=-0.4

. Which statement best interprets this result in context, including correct sign and units? (a) At

t=10

hours, the temperature is increasing at about

0.4\ ^\circ\mathrm{C}

per hour. (b) At

t=10

hours, the temperature is decreasing at about

0.4\ ^\circ\mathrm{C}

per hour. (c) At

t=10

hours, the temperature is decreasing at about

0.4

hours per

^\circ\mathrm{C}

. (d) Ten hours after midnight, the temperature equals

-0.4\ ^\circ\mathrm{C}