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To express f theta in terms of time, note that the main Ferris wheel takes 6 minutes to make a complete revolution. So the rider is 1. So when all is said and done, the height of the end wheel is given by: You do the graph.

Is h t periodic? It takes 6 min for the main wheel to make one revolution. How many revolutions does the end wheel make in the same time? Yes, the function is periodic, and the period is 12 min.

Most people would probably look at the figure and say that the maximum value of h t is 50m the height of the supporting arm, plus the radius of the main wheel, plus the radius of the end wheel. However, that is incorrect. In fact, h t can never achieve that height. Use the First Derivative Test to find the value of t that maximizes h t , then plug it into h t to find the max height.

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