408CF09assign5 - x = x(1-x 1 3 and identify the inflection...

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M408C Fall 2009 Assignment 5 Due Thursday, October 8 You should have read and understood sections 4.4, 4.5, and 4.7 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.Find the horizontal asympototes for each function below: (a) f ( x ) = x 1 + | x | . (b) f ( x ) = 3 x 4 x 2 + 1 2. Describe the concavity of f
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Unformatted text preview: ( x ) = x (1-x ) 1 3 and identify the inflection points. Find and classify all local extrema. 3. Let f ( x ) = x ( x + 3) 2 . ( i ) Describe the increasing/decreasing behavior of f and classify the local extrema. ( ii ) Describe the concavity of the graph of f and find the inflection points. ( iii ) Find the horizontal and vertical asymptotes. ( iv ) Plot the points of interest (those found above as well as x and y intercepts). ( v ) Sketch the graph of the function from the information you have determined. 4. Find the dimensions of the rectangle of greatest area that can be inscribed in a semicircle of radius r ....
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