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1) Match each of the following graphs to the appropriate conditions for Explain. y=f ( x ) 0 1 2 II. y=f ( x ) 0 1 2 III. y=f ( x ) 0 1 2 A. f ' ( x...

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1) Match each of the following graphs to the appropriate conditions for f ' and f ' ' . Explain. I. II. III. A. f ' ( x )> 0 on ( 0,2 ) ,f ' ' ( x ) < 0 on ( 0,1 ) ,f ' ' ( x )> 0 on ( 1,2 ) B. f ' ( x )> 0 on ( 0,1 ) ,f ' ( x )< 0 on ( 1,2 ) ,f ' ' ( x ) > 0 on ( 1,2 ) ,f '' ( x ) < 0 on ( 1,2 ) C. f ' ( x )> 0 on ( 0,1 ) ,f ' ( x )< 0 on ( 1,2 ) ,f ' ' ( x ) > 0 on ( 0,2 ) D. f ' ( x )> 0 on ( 0,1 ) ,f ' ( x )< 0 on ( 1,2 ) ,f ' ' ( x ) < 0 on ( 0,2 ) y = f ( x ) 2 1 0 y = f ( x ) 1 0 2 y = f ( x ) 1 0 2
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E. f ' ( x )< 0 on ( 0,1 ) ,f ' ( x )> 0 on ( 1,2 ) ,f ' ' ( x ) < 0 on ( 0,1 ) , f '' ( x ) > 0 on ( 1,2 ) Write the letter that corresponds to the correct graph: (I) __ ________ (II) __ ________ (III) __ ________ 2) Find the critical numbers for the function f ( x )= 2 x x 1 (A) x = 0, (B) x = 0, x = 1 (C) x = 2 (D) x = 1, x = 2 (E) None of the above 2) _____________
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aalexan.doc

Answer 1:
I C
II D
III A
Explanation:
The graph (I) is increasing in the interval 0,1 and decreasing in the interval 1, 2 . Also
graph is concave up throughout the interval 0, 2 Hence the correct...

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