hw10-9-1 - Homework 10/9 Identify each problem as type I:...

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Unformatted text preview: Homework 10/9 Identify each problem as type I: “Given location, find slope,” II: “Given slope, find location,” or III: “Find unknown constants.” Then solve each problem. 1. An object is dropped from a tower so that after t seconds its height above ground is h(t) = 100 − 16t2 feet. (a) What is its velocity after 2 seconds? (b) When is its velocity −60 ft/s? (c) What is its velocity at the time when it hits the ground? (d) How high is it when its velocity is −48 ft/s? 2. The graph of f (x) = 1/x has a tangent line that passes through (0, 1.5) as shown at right. Where is the point of tangency? 2 1.5 1 0.5 –1 0 1 –0.5 2 3 x –1 3. Find the slope of the tangent to y = sin(2x) at the point x = 1. 4. Find one point on the graph of y = sin(2x) where the slope of the tangent line is 1. 5. Section 3.4; problems 32, 34, 35, 36. (No sketches or graphs required.) 6. The parabola y = x2 + ax + b has a horizontal tangent at (2, −1). Find a and b. 7. Section 3.2; problem 53. 1 4 8. The graph of y = ax3 + bx2 + cx + k has horizontal tangents at (0, 1) and at (−3, 2). Find a, b, c and k . 9. A particle moves in a straight path so that its position (in meters) is given by s(t) = 1.3 sin(ωt), with t in seconds. If its velocity at time t = 0 is 0.2 m/s, what is the value of the constant ω ? What are the units on ω ? 10. Section 3.3; problem 11. Selected Answers: 1: (a) −64 ft/s; (b) 1.875 s; (c) −80 ft/s; (d) 64 ft 2: (4/3, 3/4) 3: 2 cos 2, or approximately −0.8323 √ 4: (π/6, 3/2) is one possible answer. There are many more. 5: (32) no solutions; (34) π/6 and 5π/6; (36) π/2, 5π/2, 11π/2, etc. 6: a = −4 and b = 3. 2 ...
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This note was uploaded on 10/12/2011 for the course MATH 170 taught by Professor Staff during the Fall '08 term at Boise State.

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hw10-9-1 - Homework 10/9 Identify each problem as type I:...

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