MTH_251_simonds_final_exam_200604

MTH_251_simonds_final_exam_200604 - MTH 251 Fall Term 2006...

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Page 1 of 4 MTH 251 – Fall Term 2006 F i n a l E x a m N o C a l c u l a t o r N a m e For each non-“fill in the blank” question, you must show all relevant work in a well documented manner to earn full credit for the problem. 1. Find the first derivative formula for each function and write the (simplified) formula in the provided blank. Do not show any other work – do your work on scratch paper. Your answers are going to be marked right or wrong. (2 points each.) a. If () () 2 tan f xx = , then ( ) fx = b. If 3 cos f x = , then ( ) = c. If 4 sin f = , then ( ) = d. If () ln f = , then ( ) = e. If 10 9 x =− , then ( ) = f. If 2 ln f =⎡ ⎣⎦ , then ( ) = g. If ln x x = , then ( ) = 2. On what interval(s) is the function ( ) 3 9 gx x x =+ decreasing? How do you know? (4 points) NOTE: Don’t worry about going through a formal process – just briefly tell me how you know. 3. Find the equation of the tangent line to the curve with equation 22 2 x xy y x y −= at the point ( ) 1,1 . Make sure that your conclusion is fully substantiated. (15 points) Figure 1: 2 x x y
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MTH 251 Final Exam 200604 Page 2 of 4 4. Choose the appropriate word or phrase from Table 1 that makes each given statement true.
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MTH_251_simonds_final_exam_200604 - MTH 251 Fall Term 2006...

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