MTH_251_simonds_final_exam_200604_key

MTH_251_simonds_final_exam_200604_key - MTH 251 Fall Term...

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Page 1 of 7 MTH 251 – Fall Term 2006 Final Exam – No Calculator Key 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 ( ) ( ) 2 2s e c f x = b. If 3 cos f x = , then ( ) ( ) ( ) 23 3c o s s i n f x x x =− c. If 4 sin f = , then ( ) ( ) ( ) 3 4sin cos f x = d. If () ln f = , then 1 2 fx x = e. If 10 9 x , then 2 10 x f. If 2 ln f =⎡ ⎣⎦ , then ( ) 2ln x x = g. If ln x x = , then ( ) 2 ln 1 ln x x = 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. () ( ) 32 93 9 x x g x x = +⇒ = + Since is clearly always positive, g must always be increasing; i.e., g decreases nowhere.
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MTH 251 Final Exam 200604 Key Page 2 of 7 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) 2 2 2 2 2 1,1 2 2 2 2 221 112 1 2 dd xx y yx y dx dx dy dy dy y x y y x dx dx dx dy dy dy y x y y x dx dx dx dy y x y xy dx dy x y x y dx y dy dx ⎛⎞ −+ =− + ⎜⎟ ⎝⎠ −− = = = = = 4. Choose the appropriate word or phrase from Table 1 that makes each given statement true. (2 points each) Table 1: Possible correct answers to problem 4. positive negative not positive not negative undefined zero increasing decreasing concave up concave down horizontal Obamamanic a. Along intervals where f is decreasing, f is definitely concave down b. At any point that an antiderivative of f
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This note was uploaded on 02/24/2010 for the course MATH math 251 taught by Professor Simonds during the Spring '10 term at Portland CC.

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MTH_251_simonds_final_exam_200604_key - MTH 251 Fall Term...

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