Test 3B - Test 3, Version B Math 1501, Fall 02. Prof. W....

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Test 3, Version B Math 1501, Fall 02. Prof. W. Gangbo * October 28, 2002 Student Name: Student Section: Teaching Assistant Name: Instructions. You are to work independently these exercises for the next fourty five minutes (45 mn.). You may not use any textbook or your class notes during the text. Read carefully each exercise and show all your work. * School of Mathematics, Georgia Institute of technology. 1
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Exercise 1 ( 25 points ) Assume that f ( x )= | x +1 | if - 3 x< 0 x 2 - 4 x +2 if 0 3 2 x - 7i f 3 x 4 . (a) ( 10 points ) Find the critical points of f. (b) ( 10 points ) Find the local extreme values of (c) ( 5 points ) Classify the local extreme values of 2
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Exercise 2 ( 25 points )Set f ( x )=2cos 2 x - x 2 ,x [0 ] . a) ( 5 points )Eva luate f 0 and f . b) ( 15 points ) Find the points of inflection of f. c) ( 5 points ) Describe the concavity of 3
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Exercise 3 ( 20 points ) Determine whether or not the graph of x f ( x )=4 - (2 - x ) 3 7 has a vertical tangent or a vertical cusp at c =2 . Justify your answer. 4
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Exercise 4 ( 30 points ) Assume that f ( x )=3 x 2 ,x [0 , 8] . a) ( 5 points )For P = { x 0 1 , ···
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Test 3B - Test 3, Version B Math 1501, Fall 02. Prof. W....

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