An established rollercoaster can be modelled by f:[0,3]--> R, f(x) = -x^3+3x^2-x+5, where x-axis represents the ground and the y-axis represents the height of the track above the ground. The theme park owner wishes to extend the track from the point x= 3 using a parabolic path so that the track travels underground through a tunnel and comes back to the surface at (5, 0). The point at which the extension joins the existing track needs to be smooth. Find the function of the new extension.
An established rollercoaster can be modelled by f:[0,3]--> R, f(x) = -x^3+3x^2-x+5, where x-axis represents the ground and the y-axis represents the height of the track above the ground. The theme park owner wishes to extend the track from the point x= 3 using a parabolic path so that the track travels underground through a tunnel and comes back to the surface at (5, 0). The point at which the extension joins the existing track needs to be smooth. Find the function of the new extension.
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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An established rollercoaster can be modelled by f:[0,3]--> R, f(x) = -x^3+3x^2-x+5, where x-axis represents the ground and the y-axis represents the height of the track above the ground. The theme park owner wishes to extend the track from the point x= 3 using a parabolic path so that the track travels underground through a tunnel and comes back to the surface at (5, 0). The point at which the extension joins the existing track needs to be smooth. Find the function of the new extension.
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