Calc1 old exam - x where ) ( ' = x f . 8. Find the point(s)...

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Math 211 – Test I September 23, 2005 Name: __________________ Please show all of your work. I . (5 pts each) Each of the followings shows the graph of ) ( x f y = and its tangent line at a x = . Evaluate each ) ( ' a f . A. = ) 4 ( ' f 4 2 0 2 4 6 B. 4 2 0 2 4 6 C. = ) 2 ( ' f 4 2 = ) 4 ( ' f
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0 2 4 6 II . (5 pts) Find the graph of the derivative of the given function ). ( x f y = ) ( x f y = ) ( ' x f y = III . (10pts) Answer the following questions for the given graph of ). ( x f y = -8 -6 -4 -2 0 2 4 6 8 1. Determine the sign of ) ( ' x f for all 5 x . 2. Determine the sign of ) ( ' ' x f for all 5 x . 3. Find the number of the inflection points for the graph of ). ( x f y = 4. Find the vertical asymptote(s), if exists. Otherwise, write none. 5. Find the horizontal asymptote(s), if exists. Otherwise, write none. 6. Find the number of points x where 0 ) ( = x f . 7. Find the number of points
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Unformatted text preview: x where ) ( ' = x f . 8. Find the point(s) x where ) ( ' = x f and ) ( ' ' < x f . 9. Find the point(s) x where ) ( ' ' ) ( ' x f x f = = . 10. Find the domain of ). ( x f y = IV .(7pts)Graph the function ) ( x f y = , where ) ( x f y = satisfies the following conditions: ) 4 ( ) ( f f = = and the x-axis is the horizontal asymptote for ) ( x f y = ; x-2-1 1 2 3 f---+ + + + + +-f-+ + +-+----3 -2 -1 0 1 2 3 4 V. (5pts) The graphs of , ' , f f and ' ' f are shown(not in the order). Identify each curve. VI . (8 pts) Use the limit definition to prove 5 4 ) ( ' +-= x x f , where x x x f 5 2 ) ( 2 +-= ....
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This note was uploaded on 04/04/2008 for the course CALC 181 taught by Professor Choi during the Spring '08 term at Shippensburg University of Pennsylvania.

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Calc1 old exam - x where ) ( ' = x f . 8. Find the point(s)...

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