During the first 6 days of the rainy season

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

Problem

During the first 6 days of the rainy season, the volume

V

(in thousands of cubic meters) of water in a reservoir is modeled by

V(t)=-t^{3}+6t^{2}+24t+120,

where

t

is measured in days (

0\le t\le 6

). At what time

t

is water being added to the reservoir at the greatest instantaneous rate? (a)

t\approx5.5\text{ days}

(b)

t=2\text{ days}

(c)

t=1\text{ day}

(d)

t=6\text{ days}