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practice3

# practice3 - 5 10 15 20 v(m/s 8.1 6.8 5.7 5.1 4.9(a Graph...

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Practice Exam 3 M170-003 Fall, 2006 WARNING: This not representative of your Exam 3. It’s just to keep you from downloading an old exam and making a worse mistake. 1. For f ( x ) = x 3 - x 2 - x ±nd: (a) The exact intervals on which f is increasing and the exact intervals on which it is de- creasing. (b) The x - and y -coordinates of all critical points. Then sketch a graph of f that agrees with all of your answers above. 2. For g ( x ) = 4 sin x + x 2 , with 0 x π , ±nd the exact intervals on which g is concave up and those on which it is concave down. 3. If C ( x ) = 100 xe x/ 100 + 50 x , use di²erentials to approximate C (100) - C (97). 4. Find lim x π/ 2 (2 x - π ) 2 1 - sin x 5. The velocity of a moving object (in m/s) is measured every 5 seconds and recorded in the following table: t (s)
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Unformatted text preview: 5 10 15 20 v (m/s) 8.1 6.8 5.7 5.1 4.9 (a) Graph the velocity data on the graph paper provided below. (Label your graph properly!) (b) Estimate the total change in the object’s position on the time interval 0 ≤ t ≤ 20 seconds. (c) Shade an area in your graph that matches your computation. 6. The graph of a function f is shown at right. If g ( x ) = i x f ( t ) dt , compute the following: (a) g (-2) (b) g (0) (c) g (4) (d) g ′ (2) 2 2 4 6 f(t) t 7. Find I π/ 2 ( t + 4 t 2-sin t ) dt 8. The rate of change of a certain quantity is given by f ( t ) = 3 t + 2 /t . If the quantity is 15 at time t = 10, what is the quantity at time t = 20? 1...
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