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y 052 9 sin 3 x 2 16 cos 4 x Using graphing techniques, the zeros of y 0 in the domain 0 # x # 2 p are x < 0.542, x < 1.266, x < 1.876, x < 2.600, x < 3.425, x < 4.281, x < 5.144 and x < 6.000. Graphical support: 3 2} p 4 } , } 9 4 p } 4 by [ 2 2.5, 2.5] (a) Approximately [0, 0.176], 3 0.994, } p 2 } 4 , [2.148, 2.965], 3 3.834, } 3 2 p } 4 , and 3 5.591, 2 p 4 (b) Approximately [0.176, 0.994], 3 } p 2 } , 2.148 4 , [2.965, 3.834], and 3 } 3 2 p } , 5.591 4 (c) Approximately (0.542, 1.266), (1.876, 2.600), (3.425, 4.281), and (5.144, 6.000) (d) Approximately (0, 0.542), (1.266, 1.876), (2.600, 3.425), (4.281, 5.144), and (6.000, 2 p ) (e) Local maxima at < (0.176, 1.266), 1 } p 2 } ,0 2 and (2.965, 1.266), 1 } 3 2 p } ,2 2 , and (2 p ,1); local minima at < (0, 1), (0.994, 2 0.513), (2.148, 2 0.513), (3.834, 2 1.806), and (5.591, 2 1.806) Note that the local extrema at x < 3.834, x 5 } 3 2 p } , and x < 5.591 are also absolute extrema. (f) < (0.542, 0.437), (1.266, 2 0.267), (1.876, 2 0.267), (2.600, 0.437), (3.425, 2 0.329), (4.281, 0.120), (5.144, 0.120), and (6.000, 2 0.329) Chapter 4 Review 191 Intervals 0 , x , 0.542 0.542 , x , 1.266 1.266 , x , 1.876 Sign of y 02 1 2 Behavior of y Concave down Concave up Concave down Concave up 1 1.876 , x , 2.600 Concave down 2 2.600 , x , 3.425 Intervals 3.425 , x , 4.281 4.281 , x , 5.144 5.144 , x , 6.000 Sign of y 0 121 Behavior of y Concave up Concave down Concave up Concave down 2 6.000 , x , 2 p

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13. y 95 h y 05 h Graphical support: [ 2 4, 4] by [ 2 2, 4] (a) 1 0, } ˇ 2 3 w } 4 (b) ( 2‘ , 0] and 3 } ˇ 2 3 w } , 2 (c) ( 2‘ ,0) (d) (0, ) (e) Local maximum at 1 } ˇ 2 3 w } , } 3 ˇ 16 3 w } 2 < (1.155, 3.079) (f) None. Note that there is no point of inflection at x 5 0 because the derivative is undefined and no tangent line exists at this point. 14. y 952 5 x 4 1 7 x 2 1 10 x 1 4 Using graphing techniques, the zeros of y 9 are x < 2 0.578 and x < 1.692. y 052 20 x 3 1 14 x 1 10 Using graphing techniques, the zero of y 0 is x < 1.079.
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