# hw9-7 - Math 170-010 Homework 9/7 Fall 2011 Goal • Given...

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Unformatted text preview: Math 170-010 Homework 9/7 Fall 2011 Goal: • Given tangent slope ﬁnd location by successive numerical approximation. Note: You MAY NOT use any techniques of diﬀerentiation that you might know from other classes. Every derivative must be computed by • Table of secant slopes, followed by guessing a tangent slope. Warm Up: (If you were in class on 9/6, you already did most or all of this.) 1. For f (t) = tet , compute f ′ (2). 2. Graph f . In your graph, sketch the tangent line at location t = 2. 3. If you were to guess a location where tangent slope is 10, would you look left or right of t = 2? 4. Guess a location where tangent slope is 10. Use your guess as the ﬁxed location and compute f ′ there. Use the usual table of ﬁxed end, free ends, and secant slopes. Exercises: 1. For f (x) = 5 ln x, ﬁnd where f ′ (x) = 1.5. Use a technique similar to the warm up. Keep making new guesses for the location until your tangent slope computation produces 1.50. 2. The height of a falling object is given by h(t) = 3000 − 35t − 125e−7t/25 where h is measured in feet and t is in seconds. (This is the skydiver from week one homework. At what instant in time is the object falling at −20 ft/sec? Challenge Problems: 1 1. The graph at right shows a function, f (x) = 1 x and the tangent line at location x = 2. [Warning! Graph is not to scale] (a) Compute f ′ (2). (b) Write the equation of the tangent line. [Hint: Use the slope you just computed, and the x- and y -coordinates of the point of tangency.] (c) Where does the tangent line cross the y axis 2. The graph at right shows a function, f (x) = 1 x and the tangent line at an unknown location. [Warning! Graph is not to scale] If the tangent line crosses the y -axis at 1.5, where is the point of tangency? Hints and Answers Warm Up: 1) 22.167. 3) left. 4) 1.419 would be a very good guess. Exercises: 1) x ≈ 3.333. 2) t ≈ 3.026 sec. Challenges: 1-a) 0.25; 1-b) y = 1 − 0.25x; 1-c) 1. 2) x ≈ 1.333 2 ...
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hw9-7 - Math 170-010 Homework 9/7 Fall 2011 Goal • Given...

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