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hw9-6-1

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Math 170-010 Homework 9/6 Fall 2011 Goals: Given tangent slope, determine where it is located. Do this algebraically. Do this 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 using of two methods: Table of secant slopes, followed by guessing a tangent slope. Algebraic formula for secant, followed by a limit calculation. Exercises: 1. Refer to Schaum’s Outline , Chapter 9: Problem 23. For each position function, locate all times when the velocity is exactly 1 ft/sec. 2. For f ( x ) = sin x , find one location between 0 and π/ 2 where the tangent slope is 0 . 6. Your answer should be accurate to two decimal places. [Note: This will probably require more than one round of guess-and-check. If this were a graded problem, you whould have to show me all of your guesses. I would also like to see how

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Unformatted text preview: your wrong guesses help you make better guesses.] 3. The electrical potential in a circuit is given by V ( t ) = 320 e − 3 . 1 t where t is measured in seconds and V is measured in Volts. When is the rate of change of V equal to-35 Volts/sec? Your answer should be accurate to two decimal places. [Note: As in Problem 2.] Challenge Problem: The following table gives the temperature of an object placed in a freezer as a function of time, x , in minutes. Temperature, T , is measured in degrees Celsius, ◦ C. x (minutes) 2 4 6 8 10 T ( ◦ C) 10 5.5 2.1-. 6-2 . 6-4 . 2 When is T ′ ( x ) =-2 . ◦ /min? 1 Hints and Answers Exercises: 1. (a) t =-1 sec. (b) Approximately t = 2 . 15 sec and t =-. 15 sec. (Exact values are 1 ± 2 √ 3 / 3.) (c) t =-1 . 75 sec. 2. x ≈ . 927 3. x ≈ 1 . 08 sec. Challenge : x ≈ 7 min. 2...
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