Pre-Calc Homework Solutions 134

Pre-Calc Homework Solutions 134 - 134 9 Section 4.2(b Since...

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9. [ 2 4.7, 4.7] by [ 2 3.1, 3.1] (a) f 9 ( x ) 5 x ? } 2 ˇ 4 w 1 2 w x w } ( 2 1) 1 ˇ 4 w 2 w x w 5 } 2 2 ˇ 3 x 4 w 1 2 w 8 x w } The local extrema occur at the critical point x 5 } 8 3 } and at the endpoint x 5 4. There is a local (and absolute) maximum at 1 } 8 3 } , } 3 ˇ 16 3 w } 2 or approximately (2.67, 3.08), and a local minimum at (4, 0). (b) Since f 9 ( x ) . 0 on 1 2‘ , } 8 3 } 2 , f ( x ) is increasing on 1 2‘ , } 8 3 } 4 . (c) Since f 9 ( x ) , 0 on 1 } 8 3 } ,4 2 , f ( x ) is decreasing on 3 } 8 3 } 4 . 10. [ 2 5, 5] by [ 2 15, 15] (a) g 9 ( x ) 5 x 1/3 (1) 1 } 1 3 } x 2 2/3 ( x 1 8) 5 } 4 3 x x 1 2/3 8 } The local extrema can occur at the critical points x 52 2 and x 5 0, but the graph shows that no extrema occurs at x 5 0. There is a local (and absolute) minimum at ( 2 2, 2 6 ˇ 3 2 w ) or approximately ( 2 2, 2 7.56). (b) Since g 9 ( x ) . 0 on the intervals ( 2 2, 0) and (0, ), and g ( x ) is continuous at x 5 0, g ( x ) is increasing on [ 2 2, ). (c) Since g 9 ( x ) , 0 on the interval ( 2‘ , 2 2), g ( x ) is decreasing on ( 2‘ , 2 2]. 11. [ 2 5, 5] by [ 2 0.4, 0.4] (a) h 9 ( x ) 55 } ( x x 2 2 1 2 4 4 ) 2 } 5 } ( x 1 ( x 2 2 1 )( x 4 2 ) 2 2) } The local extrema occur at the critical points, x 56 2.
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