A city's air-quality index (higher values indicate poorer air quality) is monitored…
MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A city's air-quality index A(t) (higher values indicate poorer air quality) is monitored over a 24-hour period, where t is the number of hours after midnight. The derivative of the index satisfies
• A′(t)>0 for 0<t<7
• A′(t)<0 for 7<t<15
• A′(t)>0 for 15<t<24
City officials wish to schedule a 4-hour outdoor festival during the period when air quality is most likely improving. Which schedule best meets this goal?
(a) 5 a.m.–9 a.m. (t=5 to t=9)
(b) 8 a.m.–12 p.m. (t=8 to t=12)
(c) 6 p.m.–10 p.m. (t=18 to t=22)
(d) 2 p.m.–6 p.m. (t=14 to t=18)