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Test3

# Test3 - Student's Name Test 3(Sections 3.9 4.1 4.2 4.3 4.4...

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Student’s Name: Test 3 (Sections 3.9, 4.1, 4.2, 4.3, 4.4, and 4.7) MAC2311, Section 17, Instructor: Ms. Hoa Nguyen Problem 1 ( 15pts ) A boy starts walking east at 1 600 mi/s from a point P. Twenty-five minutes later, a girl starts walking west at 1 300 mi/s from a point 3 mi due south of P. At what rate are the people moving apart 5 minutes after the girl starts walking? Problem 2 ( 10pts ) Find the critical numbers of the function g ( x ) = 100 - x 2 . Problem 3 ( 15pts ) Find the absolute maximum, absolute minimum, local maximum and local minimum values of f ( x ) = sin(5 x ) + cos(5 x ) on the interval [0 , π 10 ]. Problem 4 ( 10pts ) At 4:15 pm, a biker starts her travel. At 7:15 pm, she has traveled 45 km. So at some time between 4:15 and 7:15, her speedometer must have read x km/h. Find x . Problem 5 ( 10pts ) Find the inflection points of the function f ( x ) = 8 x + 3 - 2 cos x , π 2 < x < 7 π 2 . 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. ( 2pts )

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