Derivatives are slopes…

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Presentation transcript:

Derivatives are slopes… Part (a) Whenever you’re asked for a “rate of change”, it will involve a derivative. Derivatives are slopes… L’(t) = 150 - 126 7 - 4 = 3 24 8 At 5:30 PM, the line is increasing by 8 people per hour.

= ½ (1) (120+156) + ½ (2) (156+176) + ½ (1) (176+126) ½ (2) (156+176) Part (b) 1 3 4 = 138 + 332 + 151 = 155.25 people = ½ (1) (120+156) + ½ (2) (156+176) + ½ (1) (176+126) ½ (2) (156+176) ½ (1) (176+126)

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

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 = 972.784 973 tickets were sold by 3:00 PM.