Test2s - MATH 1501 Test 2 October 12, 2009 No books or...

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Unformatted text preview: MATH 1501 Test 2 October 12, 2009 No books or notes allowed. No laptop, graphic calculator or wireless devices allowed. Write clearly. Show your work and justify your answers Name: Question: 1 2 3 4 5 Total Points: 20 11 12 42 15 100 Score: MATH 1501 Test 2 October 12, 2009 1. Evaluate each of the following statements as true or false. Justify your answer by either giving a brief explanation or providing a counterexample as appropriate. (a) (10 points) There exists a differentiable function f such that f (0) =- 1, f (2) = 4 and f ( x ) &lt; 2 for all x . Solution: False. If f (0) =- 1 and f (2) = 4 by the Mean Value Theorem there exists a c in [0 , 2] such that f ( c ) = f (2)- f (0) 2 = 5 2 &gt; 2 . (1) This contradict the assumption that f ( x ) &lt; 2 for all x . (b) (10 points) If f (0) = 0 and f (0) = 0, then f has neither a local maximum nor a local minimum at x = 0. Solution: False. Let f ( x ) = x 4 . Then f (0) = 0 and f (0) = 0 but x = 0 is a local minimum....
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Test2s - MATH 1501 Test 2 October 12, 2009 No books or...

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