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hw9-19 - (d How high is it when its velocity is-48 ft/s 1 6...

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Math 170-010 Homework 9/19 Fall 2011 Goal: Use your understanding of derivatives to work more complicated problems. Learn to recognize whether a problem requires that you compute slope, given location, or that you find location, given slope. Note: You can use any of the easy derivative rules from the list we have developed so far. If you encounter a function NOT on the list, you have to resort to secant slope methods. Note: Before you start each problem, try to identify each problem as Type 1: “Given location, find slope”, or Type 2: “Given slope, find location”. Exercises: 1. From Schaum’s , Chapter 9, Problem 19. 2. For each function in Problem 19, determine all locations where there is a slope of exactly - 2. 3. From Schaum’s , Chapter 9, Problem 21. 4. From Schaum’s , Chapter 9, Problem 22. 5. An object is dropped from a tower so that after t seconds its height above ground is h ( t ) = 100 - 16 t 2 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?
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Unformatted text preview: (d) How high is it when its velocity is-48 ft/s? 1 6. The graph of f ( x ) = 1 /x has a tangent line that passes through (0 , 1 . 5) as shown at right. (a) Where is the point of tangency? (b) Find the equation of the tangent line at the point (2 , . 5). Sketch this line in the graph at right. –1 –0.5 0.5 1 1.5 2 –1 1 2 3 4 x Challenge Problems: 1. In the ±gure the below the curve is y = sin x and the line is tangent to the curve at x = 3 π/ 4. Find the x-intercept of the line. 2 2. In the fgure the below the curve is y = sin x and the tangent line has x-intercept at 5 π/ 4. Find the point o± tangency. Hints and Answers Exercises: 1. All Type 1. 2. All Type 2. (a) x = 1 / 5; (b) x =-1 ± √ 2; (c) x =-2 ,-4. 3. Type 2. 4. Type 1. 5. (a) Type 1,-64 ±t/s; (b) Type 2, 1.875 s; (c) Type 1,-80 ±t/s; (d) Type 2, 64 ±t. 6. (a) Type 2, (4 / 3 , 3 / 4); (b) Type 1, y =-x/ 4 + 1. Challenge: 1. Type 1, x = 3 π/ 4 + 1 ≈ 3 . 356. 2. Type 2, x ≈ 2 . 063. 3...
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