FinalExam_W10_Solutions

# FinalExam_W10_Solutions - Math 115 Final Exam Name...

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Math 115 / Final (April 23, 2010) page 2 1 . [12 points] For the following statements, select True if the statement is ALWAYS true, and select False otherwise. No explanations are required. a . [2 points] If f is a di±erentiable function and f (5 . 1) f (5) 0 . 1 = - 3, then f (5) = - 3. True False b . [2 points] If g is a continuous function, then i 20 1 g ( x ) dx = i 100 1 g ( x ) dx + i 20 100 g ( x ) dx . True False c . [2 points] If h is an odd function and is continuous everywhere, then h is invertible. True False d . [2 points] If k is a di±erentiable function and is always concave up, then k ( a ) k ( b ) - k ( a ) b - a whenever a < b . True False e . [2 points] If is a continuous function, then i 3 2 ( t ) dt i 4 2 ( t ) dt . True False f . [2 points] Suppose m is a twice di±erentiable function. If m ′′ (5) = 0, then m does not have an in²ection point at x = 5. True False
Math 115 / Final (April 23, 2010) page 3 2 . [12 points] Use the graph of the function f and the table of values for the function g to answer the questions below. Each problem requires only a small amount of work, but you must show it. 1 2 3 4 5 6 10 20 30 f ( x ) x -20 -10 0 10 20 30 g(x) 0 4 0 -18 -56 -120 g’(x) 6 1 -10 -27 -50 -79 a . [3 points] Write a formula for the local linearization of g near x = 10 and use it to ap- proximate g (10 . 1).

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## This note was uploaded on 01/28/2012 for the course MATH 115 taught by Professor Blakelock during the Fall '08 term at University of Michigan.

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FinalExam_W10_Solutions - Math 115 Final Exam Name...

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