team hw 10HW12#44 - Chapter 4 Review#44(a The mouse changes...

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Chapter 4 Review #44 (a) The mouse changes direction at approximately t=17, 23, 27. To determine this, we look at where the graph changes from positive to negative, or vice versa. At t=17, the graph goes from positive to negative, or in terms of position, the mouse changes from moving right to moving left. At t=23, the mouse changes from moving left to moving right, and at t=27, the mouse changes from moving right to moving left. (b) The mouse is moving most rapidly to the right where there is a maximum on the graph, so at approximately t=10. He is moving most rapidly to the left where there is a minimum, so around t=40. (c) From looking at the graph, we can determine when the mouse is farthest to the right of center where the area under the curve is the greatest positive value. In this case the greatest area under the curve is found on the interval (0,17), so the greatest area occurs when t=17. Therefore at t=17, the mouse is the farthest to the right of center. To find the time at which the mouse is farthest to the left of center, we must find where the greatest negative area under the curve occurs.
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