Section 4.2 AN21 19. Step 1: = y x5 4 Step 2: x-intercepts: − − 3, 2, 0, 2; y-intercept: 0 Step 3: − − 3, 2, 0, 2: multiplicity 1, crosses Step 4: 50 24 270 3 Step 5: ( ) ( ) ( ) − − − − 2.57, 14.39 ; 0.93, 30.18 ; 1.25, 64.75 Step 6: (2, 0) (0, 0) (20.93, 30.18) (22, 0) (23, 0) (1.25, 264.75) y x 2 23 260 40 (22.57, 214.39) Step 7: Range: [ ) − ∞ 64.75, Step 8: Increasing on [ ] − − 2.57, 0.93 and [ )∞ 1.25, Decreasing on ( ] −∞ −, 2.57 and [ ] −0.93, 1.25 21. Step 1: = y x5 Step 2: x-intercepts: 0, 2; y-intercept: 0 Step 3: 0: multiplicity 2, touches; 2: multiplicity 1, crosses Step 4: 30 23 230 3 Step 5: ( ) ( ) − 0, 0 ; 1.48, 5.91 Step 6: y 160 x 5 (0, 0) (2, 0) (3, 108) (21, 212) (1.48, 25.91) Step 7: Range: ( ) −∞∞, Step 8: Increasing on ( ] −∞, 0 and [ )∞ 1.48, Decreasing on [ ] 0, 1.48 23. Step 1: = y x3 Step 2: 2 22 22 2 Step 3: x-intercepts: − − 1.26, 0.20, 1.26; y-intercept: −0.31752 Step 4: Step 5: ( ) ( ) − − 0.80, 0.57 ; 0.66, 0.99 Step 6: y 2.5 x 2.5 (1.5, 1.13) (1.26, 0) (0.66, 20.99) (20.5, 0.40) (20.80, 0.57) (20.20, 0) (21.26, 0) (21.5, 20.86) (0, 20.32) Step 7: ( ) −∞∞ Range: , Step 8: Increasing on ( ] −∞ −, 0.80 and [ )∞ 0.66, Decreasing on [ ] −0.80, 0.66 25. Step 1: = y x3 Step 2: 10 24 210 2 Step 3: x-intercepts: −3.56, 0.50; y-intercept: 0.89 Step 4: Step 5: ( ) ( ) −2.21, 9.91 ; 0.50, 0 Step 6: y 10 x 1 (21, 5.76) (1, 1.14) (0.5, 0) (0, 0.89) (22.21, 9.91) (23.56, 0) (23.9, 26.58) Step 7: ( ) −∞∞ Range: , Step 8: Increasing on ( ] −∞ −, 2.21 and [ )∞ 0.50, Decreasing on [ ] −2.21, 0.50 27. Step 1: = y x4 Step 2: 3 22 22 2 Step 3: x-intercepts: − − 1.5, 0.5, 0.5, 1.5; y-intercept: 0.5625 Step 4: Step 5: ( ) ( ) ( ) − − − 1.12, 1 ; 1.12, 1 ; 0, 0.56 Step 6: y 5 x 2.5 (21.5, 0) (20.5, 0) (21.75, 2.29) (21, 20.94) (21.12, 21) (1.12, 21) (1, 20.94) (1.75, 2.29) (1.5, 0) (0.5, 0) (0, 0.56) Step 7: [ ) − ∞ Range: 1, Step 8: Increasing on [ ] −1.12, 0 and [ )∞ 1.12, Decreasing on ( ] −∞ −, 1.12 and [ ] 0, 1.12 29. Step 1: = y x2 4 Step 2: 6 22 25 2 Step 3: x-intercepts: −1.07, 1.62; y-intercept: −4 Step 4: Step 5: ( ) − − 0.42, 4.64 Step 6: y 5 x 2 (21.25, 4.22) (21.07, 0) (20.42, 24.64) (0, 24) (1.75, 1.83) (1.62, 0) Step 7: [ ) − ∞ Range: 4.64, Step 8: Increasing on [ ) − ∞ 0.42, Decreasing on ( ] −∞ −, 0.42
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