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MATH 1450 Spring 2010 Quiz 5 Solutions

MATH 1450 Spring 2010 Quiz 5 Solutions - bottomed out and...

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MATH 1450, QUIZ 5 SOLUTIONS, 18 FEB., 2010 (1) Fill in the blanks: The expression lim h 0 1 / (1 + h ) 2 - 1 h represents the of the function f ( x ) = , at the point x = . The expression is the derivative of the function f ( x ) = 1 x 2 , at the point x = 1. ( 1) Fill in the blanks: The expression lim h 0 1 / (2 + h ) 2 - 1 / 2 h represents the of the function f ( x ) = , at the point x = . The expression is the derivative of the function f ( x ) = 1 x 2 , at the point x = 2. (2) Sketch the graph of a function y = f ( x ), continuous on the interval [0 , 4] and satisfying the conditions: f ( x ) < 0 for 0 < x < 1 f ( x ) > 0 for 1 < x < 2 f ( x ) = 0 for 2 < x < 4 As you draw the graph west-to-east, starting at x = 2, the graph slopes downhill until you reach x = 1. At this point the graph has
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Unformatted text preview: bottomed out and starts going uphill. When you reach x = 2, level o± and proceed due east until x = 4. ( 2) Sketch the graph of a function y = f ( x ), continuous on the interval [0 , 4] and satisfying the conditions: • f ′ ( x ) > 0 for 0 < x < 1 • f ′ ( x ) < 0 for 1 < x < 2 • f ′ ( x ) = 0 for 2 < x < 4 As you draw the graph west-to-east, starting at x = 2, the graph slopes uphill until you reach x = 1. At this point the graph has 1 topped out and starts going downhill. When you reach x = 2, level of and proceed due east until x = 4....
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