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Unformatted text preview: Students Name: Make-up Test 3 (Sections 3.9, 4.1, 4.2, 4.3, 4.4, and 4.7) MAC2311, Section 17, Instructor: Ms. Hoa Nguyen (firstname.lastname@example.org) Problem 1 ( 15pts ) Two bikes start moving from the same point. One travels south at 3 mi/h and the other travels west at 4 mi/h. At what rate is the distance between the bikes increasing one hour later? Problem 2 ( 10pts ) Find the critical numbers of the function g ( x ) = 81- x 2 . Problem 3 ( 15pts ) Find the absolute maximum, absolute minimum, local maximum and local minimum values of f ( x ) = sin(6 x ) + cos(6 x ) on the interval [0 , 18 ]. Problem 4 ( 10pts ) If f (2) = 5 and f ( x ) 1 for 2 x 7, how small can f (7) possibly be? Problem 5 ( 10pts ) Find the inflection points of the function f ( x ) = 8 x + 3- 2 sin x , 0 < x < 3 . Problem 6 ( 20pts ) Consider the equation f ( x ) =- 2 x 3- 3 x 2 + 12 x- 1. a) Find the interval(s) on which f is increasing. ( 2pts ) b) Find the interval(s) on which f is decreasing. (is decreasing....
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- Fall '08