A drone’s altitude above sea level

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A drone’s altitude above sea level,

h(t)

meters, is recorded

t

minutes after takeoff. The function

h

is continuous and differentiable for

0\le t\le 12

. Sensor data show

h(0)=50

h(4)=270

h(9)=270

, and

h(12)=140

. Which statement must be true? (a) At some time between

0

and

4

minutes, the drone’s vertical velocity was exactly

60\text{ m/min}

. (b) At some time between

4

and

9

minutes, the drone’s vertical velocity was

0\text{ m/min}

. (c) For every time between

9

and

12

minutes, the drone’s vertical velocity was negative. (d) There is no time between

0

and

12

minutes at which the drone’s vertical velocity equaled

40\text{ m/min}