At 8:00 A.M. a pool contains 200 liters of water. At 11:00 A.M. the amount has…
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
At 8:00 A.M. a pool contains 200 liters of water. At 11:00 A.M. the amount has increased to 260 liters. The volume of water is modeled by a function W(t) (in liters), where t is measured in hours after 8:00 A.M. and W is continuous and differentiable on 0≤t≤3. Which of the following statements must be true?
(a) For every t in 0≤t≤3, W′(t)=20 liters per hour.
(b) For every t in 0≤t≤3, W′(t)>20 liters per hour.
(c) At some time between 8:00 A.M. and 11:00 A.M., W′(t)=20 liters per hour.
(d) At some time between 8:00 A.M. and 11:00 A.M., W′(t)=60 liters per hour.