408CF09assign4

# 408CF09assign4 - t(measured in seconds is given by y t =...

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M408C Fall 20089 Assignment 4 Due Thursday, October 1 You should have read and understood sections 3.8, 4.1, 4.2, and 4.3 before completing this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. 1. A light is attached to the wall of a building 64 feet above the ground. A ball is dropped from the same height, but 20 feet away from the side of the building. The height y of the ball at time
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Unformatted text preview: t (measured in seconds) is given by y ( t ) = 64-16 t 2 . How fast is the shadow of the ball moving along the ground after 1 second? 2. Let f ( x ) = x √ 4-x 2 for-2 ≤ x ≤ 2. (a) Find all critical numbers of f . (b) Find the absolute maximum and absolute minimum of f . 3. Graph the function f ( x ) = | 2 x-1 | -3 and compute the derivative. Verify that f (-1) = 0 = f (2) any yet f ( x ) is never 0. Explain how this does not violate Rolle’s Theorem. 4. Let f ( x ) = x + 2cos x , 0 ≤ x ≤ 2 π . (a) Find the intervals on which f is increasing or decreasing. (b) Identify all local extreme values of f . (c) Find the intervals of concavity and identify the inﬂection points....
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