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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.
 Fall '08
 STAFF
 Calculus, Slope

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