Concept explainers
a.
Find the equation of the tangent lines at the given point.
a.
Answer to Problem 86E
The equation of tangent line is
Explanation of Solution
Given:
The given cycloid
Calculation:
Find the slope.
Apply formula
Apply
Use derivative rule
Apply difference rule
Use derivative rule
At
Find the value of value of
Now use point-slope form for the tangent equations.
Hence the equation of tangent line is
b.
Find the horizontal and vertical tangent line points on the curve.
b.
Answer to Problem 86E
The tangent is horizontal at the point
Explanation of Solution
Given:
The given cycloid
Calculation:
Find the slope.
Apply formula
Apply difference rule
Use derivative rule
Apply difference rule
Use derivative rule
For the horizontal tangent line.
Substitute
For vertical tangent line
Substitute
Hence the tangent is horizontal at the point
c.
Draw a graph for the cycloid for the given value of
c.
Explanation of Solution
Given:
The given cycloid
Calculation:
At
Theequation of tangent line is
Hence the graph of the cycloid is given below.
The tangents are
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning