To construct: the equations of two parabola and graph them and check is they are everywhere equidistant and if so in what sense.
Explanation of Solution
Given Information:
Use the concept of the derivative to define what it might mean for two parabolas to be parallel.
Calculation:
Two parabolas are parallel is they have the same derivative at every value of
As the derivative of any function at any function can be given by the slope of the tangent at that point so this means that their tangent lines are parallel at each value of
For example, two such parabolas are
Plot the graph of two parabolas.
The parabolas are everywhere equidistant as long as the distance between them is always measured along the vertical line, which will be perpendicular to the tangent at that point.
Chapter 2 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning