a.
Explain that the given curve has two tangent lines at the given point.
a.
Answer to Problem 85E
The equation of tangent lines are
Explanation of Solution
Given:
The given equations are
Calculation:
Find the slope.
Apply formula
Apply differencerule
Use derivative rule
Use derivative rule
Find the value of the parameter
At
At
Now,
Slope at
Slope at
There are two different tangents at the given point, because there is two different slope values.
Now use point-slope form for the tangent equations.
Hence the equation of tangent lines are
b.
Find the horizontal and vertical tangent line points on the curve.
b.
Answer to Problem 85E
The tangents are horizontal at the points
Explanation of Solution
Given:
The given equations are
Calculation:
Find the slope.
Apply formula
Apply
Use derivative rule
Use derivative rule
For the horizontal tangent line.
Substitute
Substitute
For vertical tangent line
Substitute
Hence the tangents are horizontal at the points
c.
Draw a graph for the part
c.
Explanation of Solution
Given:
The given equations are
Calculation:
Find the slope.
Apply formula
Apply difference rule
Use derivative rule
Use derivative rule
For the horizontal tangent line.
Substitute
Substitute
For vertical tangent line
Substitute
Draw a table for the curve
Hence the graph of the curve is given below.
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- 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