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64. 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 (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation. Highway B(1000, 90) A(-1000, 60) 6% grade 4% grade 50 ft Not drawn to scale (a) Design a section of highway connecting the hillsides modeled by the function f(x) = ax³ + bx² + cx + d, -1000 s xs 1000. 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.

64. 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 (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation. Highway B(1000, 90) A(-1000, 60) 6% grade 4% grade 50 ft Not drawn to scale (a) Design a section of highway connecting the hillsides modeled by the function f(x) = ax³ + bx² + cx + d, -1000 s xs 1000. 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.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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64. 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 (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation. Highway B(1000, 90) A(-1000, 60) 6% grade 4% grade 50 ft Not drawn to scale (a) Design a section of highway connecting the hillsides modeled by the function f(x) = ax³ + bx² + cx + d, -1000 s xs 1000. 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:64. 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 (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation. Highway B(1000, 90) A(-1000, 60) 6% grade 4% grade 50 ft Not drawn to scale (a) Design a section of highway connecting the hillsides modeled by the function f(x) = ax³ + bx² + cx + d, -1000 s xs 1000. 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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