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Fall 2005 Solutions

# Fall 2005 Solutions - MATH 115 FIRST MIDTERM EXAM NAME...

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2 1. (2 points each, no partial credit) Circle “True” or “False” for each of the following problems. Circle “True” only if the statement is always true. No explanation is necessary. (a) If A and B are positive constants, then the function f ( x ) = log( | Ax + B | ) has a vertical asymptote at x = B/A . True False (b) If an exponential function of t , in years, has decreased to 60% of the original value in two years, in four years it will decrease to 30% of the original value. True False (c) If h ( x ) = 1 . 3(0 . 5) x then the derivative, h , is decreasing for all x . True False (d) The functions sin( e x ) and e sin ( x ) are inverses of each other. True False (e) If w is a continuous function for all x , then lim h 0 w ( x + h ) w ( x ) h exists for all x . True False (f) If f ′′ ( x ) > 0 on the interval [ a, b ], then the average rate of change of f ( x ) on the interval [ a, b ] is greater than f ( x ) for all a < x < b . True False
3 2. (12 points) The graph of the derivative function, f , is given below. List all of the marked x -values, if any, from the figure for which the following statements are true. If no marked x -values apply, write “none.” f ( x ) x y x 1 x 2 x 3 x 4 x 5 (a) The value of f ( x ) is greatest

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