mth_251_simonds_final_exam_200704

mth_251_simonds_final_exam_200704 - MTH 251 Final Exam Fall...

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MTH 251 Final Exam – Fall Term 2007 Page 1 of 10 N a m e This is a no calculator test 1. Find the formula for the first derivative of each of the following functions. You do not need to show the intermediate steps (although it can help with partial credit if your formula is wrong). You do need to use proper notation on both sides of the equal sign. (17 points total) a. () 7s i n yx x = b . ( ) 6 ln 6 t ft = c. 3 5 2 2 + = x x z d . () ( ) 12 he π θ =+
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MTH 251 Final Exam – Fall Term 2007 Page 2 of 10 2. State the inflection points for the function ( ) ( ) ( ) 4 55 fx x x = −+ after first constructing a concavity table for f . Show all relevant work in an organized manner. (14 points)
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MTH 251 Final Exam – Fall Term 2007 Page 3 of 10 3. Sketch onto Figure 1 a continuous function f that passes through the point () 0,3 that satisfies all of the properties described in tables 1 and 2. (8 points) 4. Find the critical numbers for the function ( ) ( ) cos 2 gt t t =− over [ ] π 2 , 0 . Show all relevant work in an organized manner. (8 points) Table 1: Sign Analysis for f x interval f x 3 , negative 1 , 3 positive , 1 negative Table 2: Sign Analysis for f x ′′ interval f x 3 , negative 4 , 3 negative , 4 positive Figure 1
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MTH 251 Final Exam – Fall Term 2007 Page 4 of 10 5. Consider the continuous function f whose first derivative, () yf x = , is shown in Figure 2. Answer each of the following questions in reference to this function.
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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_200704 - MTH 251 Final Exam Fall...

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