1. Derivatives are slopes…
Part (a)
Whenever you’re asked for a “rate of change”, it will involve a derivative.
Derivatives are slopes…
L’(t) =
7 - 4 = 3 24 8
At 5:30 PM, the line is increasing by 8 people per hour.

2. = ½ (1) (120+156) + ½ (2) (156+176) + ½ (1) (176+126) ½ (2) (156+176)
Part (b) 1 3 4 =
= people
= ½ (1) ( ) + ½ (2) ( ) + ½ (1) ( )
½ (2) ( )
½ (1) ( )

3. Similarly, there’s a max on (4,8) and a min on (3,7).
Part (c)
-Based on the data in the chart, the graph would look something like this…
L’(t) must be zero at least 3 times.
Since L(3) > L(1) and L(3) > L(4), there must be a max between L(1) and L(4).
Similarly, there’s a max on (4,8) and a min on (3,7). 9
120
156
176
126
150 80

4. 973 tickets were sold by 3:00 PM.
Part (d)
r(t) = 550t e-t/2 3
550t e-t/2 dt
# of tickets sold =
973 tickets were sold by 3:00 PM.