Pre-Calc Homework Solutions 148

Pre-Calc Homework Solutions 148 - 148 24. y y Section 4.3 x...

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24. y 5 x 3/4 (5 2 x ) 5 5 x 3/4 2 x 7/4 y 95 } 1 4 5 } x 2 1/4 2 } 7 4 } x 3/4 5 } 15 4 x 2 1/4 7 x } y 052} 1 1 5 6 } x 2 5/4 2 } 2 1 1 6 } x 2 1/4 5 } 2 3 1 ( 6 7 x x 5 1 /4 5) } Since y 0, 0 for all x . 0, the graph of y is concave down for x . 0. Graphical support: [0, 8] by [ 2 6, 6] (a) 3 0, } 1 7 5 } 4 (b) 3 } 1 7 5 } , 2 (c) None (d) (0, ) (e) Local (and absolute) maximum: 1 } 1 7 5 } , 1 } 1 7 5 } 2 3/4 ? } 2 7 0 } 2 < 1 } 1 7 5 } , 5.06 2 ; local minimum: (0, 0) (f) None 25. y 5 x 1/3 ( x 2 4) 5 x 4/3 2 4 x 1/3 y 4 3 } x 1/3 2 } 4 3 } x 2 2/3 5 } 4 3 x x 2 2/3 4 } y 05 } 4 9 } x 2 2/3 1 } 8 9 } x 2 5/3 5 } 4 9 x x 1 5/3 8 } Graphical support: [ 2 4, 8] by [ 2 6, 8] (a) [1, ) (b) ( 2‘ ,1] (c) ( 2‘ , 2 2) and (0, ) (d) ( 2 2, 0) (e) Local minimum: (1, 2 3) (f) ( 2 2, 6 ˇ 3 2 w ) < ( 2 2, 7.56) and (0, 0) 26. y 5 x 1/4 ( x 1 3) 5 x 5/4 1 3 x 1/4 y 5 4 } x 1/4 1 } 3 4 } x 2 3/4 5 } 5 4 x x 1 3/4 3 } Since y 9. 0 for all x . 0, y is always increasing on its domain x $ 0. y 1 5 6 } x 2 3/4 2 } 1 9 6 } x 2 7/4 5 } 5 1 x 6 x 2 7/4 9 } Graphical support: [0, 6] by [0, 12] (a) [0, ) (b) None (c) 1 } 9 5 } , 2 (d) 1 0, } 9 5 } 2 (e) Local (and absolute) minimum: (0, 0) (f) 1 } 9 5 } , } 2 5 4 } ? ! 4 } 9 5 } § 2 < 1 } 9 5 } , 5.56 2 27. We use a combination of analytic and grapher techniques to solve this problem. Depending on the viewing window chosen, graphs obtained using NDER may exhibit strange
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