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Pre-Calc Homework Solutions 129

Pre-Calc Homework Solutions 129 - y is undefined There is a...

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19. [ 2 2, 6] by [ 2 2, 4] Minimum value is 1 at x 5 2. 20. [ 2 6, 6] by [ 2 2, 7] To find the exact values, note that y 9 5 3 x 2 2 2, which is zero when x 5 6 ! } 2 3 } § . Local maximum at 1 2 ! } 2 3 } § , 4 1 } 4 ˇ 9 6 w } 2 < ( 2 0.816, 5.089); local minimum at 1 ! } 2 3 } § , 4 2 } 4 ˇ 9 6 w } 2 < (0.816, 2.911) 21. [ 2 6, 6] by [ 2 5, 20] To find the exact values, note that y 9 5 3 x 2 1 2 x 2 8 5 (3 x 2 4)( x 1 2), which is zero when x 5 2 2 or x 5 } 4 3 } . Local maximum at ( 2 2, 17); local minimum at 1 } 4 3 } , 2 } 4 2 1 7 } 2 22. [ 2 6, 6] by [ 2 4, 4] Note that y 9 5 3 x 2 2 6 x 1 3 5 3( x 2 1) 2 , which is zero at x 5 1. The graph shows that the function assumes lower values to the left and higher values to the right of this point, so the function has no local or global extreme values. 23. [ 2 4, 4] by [ 2 2, 4] Minimum value is 0 at x 5 2 1 and at x 5 1. 24. [ 2 4.7, 4.7] by [ 2 3.1, 3.1] To confirm that there are no “hidden” extrema, note that y 9 5 2 ( x 2 2 1) 2 2 (2 x ) 5 } ( x 2 2 2 2 x 1) 2 } which is zero only at x 5 0 and is undefined only where
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Unformatted text preview: y is undefined. There is a local maximum at (0, 2 1). 25. [ 2 1.5, 1.5] by [ 2 0.5, 3] The minimum value is 1 at x 5 0. 26. [ 2 4.7, 4.7] by [ 2 3.1, 3.1] The actual graph of the function has asymptotes at x 5 6 1, so there are no extrema near these values. (This is an example of grapher failure .) There is a local minimum at (0, 1). 27. [ 2 4.7, 4.7] by [ 2 3.1, 3.1] Maximum value is 2 at x 5 1; minimum value is 0 at x 5 2 1 and at x 5 3. 28. [ 2 4, 4] by [ 2 80, 30] Minimum value is 2} 11 2 5 } at x 5 2 3; local maximum at (0, 10); local minimum at 1 1, } 1 2 3 } 2 29. [ 2 5, 5] by [ 2 0.7, 0.7] Maximum value is } 1 2 } at x 5 1; minimum value is 2} 1 2 } at x 5 2 1. Section 4.1 129...
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