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Unformatted text preview: 2. 3 x 2 2 6 . 3 x 2 . 6 x 2 . 2 x , 2 2 w or x . 2 w Intervals: ( 2 , 2 2 w ) < ( 2 w , ) 3. Domain: 8 2 2 x 2 $ 8 $ 2 x 2 4 $ x 2 2 2 # x # 2 The domain is [ 2 2, 2]. 4. f is continuous for all x in the domain, or, in the interval [ 2 2, 2]. 5. f is differentiable for all x in the interior of its domain, or, in the interval ( 2 2, 2). 6. We require x 2 2 1 0, so the domain is x 6 1. 7. f is continuous for all x in the domain, or, for all x 6 1. 8. f is differentiable for all x in the domain, or, for all x 6 1. 9. 7 5 2 2( 2 2) 1 C 7 5 4 1 C C 5 3 10. 2 1 5 (1) 2 1 2(1) 1 C 2 1 5 3 1 C C 5 2 4 Section 4.2 Exercises 1. (a) f 9 ( x ) 5 5 2 2 x Since f 9 ( x ) . 0 on 1 2 , } 5 2 } 2 , f 9 ( x ) 5 0 at x 5 } 5 2 } , and f 9 ( x ) , 0 on 1 } 5 2 } , 2 , we know that f ( x ) has a local maximum at x 5 } 5 2 } . Since f 1 } 5 2 } 2 5 } 2 4 5 } , the local maximum occurs at the point 1 } 5 2 } , } 2 4 5 } 2 . (This is also a global maximum.) (b) Since f 9 ( x ) . 0 on...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.
 Fall '08
 GERMAN
 Critical Point

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