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 (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation.

(a) Design a section of highway connecting the hillsides modeled by the function

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.

Transcribed Image Text:

Highway A(-1000, 60) 6% grade Not drawn to scale B(1000, 90) 4% grade 50 ft X