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Highway Design A section of highway connecting two hillsides with grades of 6% and 4% is to be built between two points that are separated by a horizontal distance of 2000 feet (sec figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation.
(a) Find the cubic function
that describes the section of highway connecting the hillsides. At points A and B, the slope of the model must match the grade of the hillside.
(b) Use a graphing utility to graph the model.
(c) Use a graphing utility to graph the derivative of the model.
(d) Determine the grade at the steepest part of the transitional section of the highway.
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Calculus (MindTap Course List)
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