2 t free response solutions 2004 ab form b 13 question

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Unformatted text preview: 2 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. Don’t forget to round. 2. To keep things simple, you might as well take all the points where R(t) = 0 on 5π 15π [0, 31], namely at t = and t = , plus both endpoints, and compare the 2 2 number of mosquitoes at these four times. 2 t FREE-RESPONSE SOLUTIONS ~ 2004 AB (FORM B) 13 Question 3 40 (b) ∫ 0 ∫ (a) 0 40 v(t ) dt ≈ 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 Rolle’s theorem (or the Mean Value Theorem), acceleration, which is v′(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 ′(23) ≈ −0.408 miles/min2. (d) Average velocity = 1 40 1 40 t 7t ∫0 f (t ) dt = 40 ∫ 0 6 + cos 10 + 3sin 40 dt 40 ≈ 5.916 miles/min. 14 FREE-RESPONSE SOLUTIONS ~ 2004 AB (FORM B) Question 4 (a) f ′ 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) = ...
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