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5
964, the number of mosquitoes at t = 31 (from Part (c)), so 1039 is the maximum. R(t) > 0 for 0 < t < Notes: 1. Donâ€™t forget to round. 2. To keep things simple, you might as well take all the points where R(t) = 0 on
5Ï€
15Ï€
[0, 31], namely at t =
and t =
, plus both endpoints, and compare the
2
2
number of mosquitoes at these four times. 2 t FREERESPONSE SOLUTIONS ~ 2004 AB (FORM B) 13 Question 3
40 (b) âˆ« 0 âˆ« (a) 0 40 v(t ) dt â‰ˆ 40
( v(5) + v(15) + v(25) + v(35) ) = 10 ( 9.2 + 7.0 + 2.4 + 4.3) = 229 miles.
4 v(t ) dt is the distance in miles traveled by the plane from 0 to 40 minutes. v(0) = v(15) and v(25) = v(30). By Rolleâ€™s theorem (or the Mean Value Theorem),
acceleration, which is vâ€²(t ) , must equal 0 at least once on each of the intervals
[0, 15] and [25, 30]. The answer is 2. (c) The acceleration at t = 23 is f â€²(23) â‰ˆ âˆ’0.408 miles/min2. (d) Average velocity =
1 40
1 40 t 7t âˆ«0 f (t ) dt = 40 âˆ« 0 6 + cos 10 + 3sin 40 dt
40 â‰ˆ 5.916 miles/min. 14 FREERESPONSE SOLUTIONS ~ 2004 AB (FORM B) Question 4
(a) f â€² changes from increasing to decreasing at x = 1 and from decreasing to
increasing x = 3. Therefore, there are two points of inflection, at x = 1 and x = 3. (b) f ( x) = âˆ...
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 Fall '11
 Mr.Snickles
 Calculus, Derivative, FREERESPONSE SOLUTIONS, Skylight Publishing

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