a.
To find: The slope of the curve at the given point.
a.
Answer to Problem 9E
Explanation of Solution
Given information:
The function is
Concept used:
Slope of any function f at any point a is given by:
Calculation:
Slope
Conclusion:
The slope of the curve at the given point is
b.
To find: the equation of the tangent line.
b.
Answer to Problem 9E
Explanation of Solution
Given information:
The function is
Concept used:
For the equation for the tangent line to
Then find the slope of the tangent line at
The equation of the tangent line is
Calculation:
From part (a) it is obtained that slope at
Find
Hence
Put
Hence the equation of tangent line is
c.
To find: The equation of the normal.
c.
Answer to Problem 9E
Explanation of Solution
Given information:
The function is
Concept used:
If the slope of a line is m, then the slope of the normal will be
Calculation:
For
Hence the equation of the normal is
d.
To graph: The curve, tangent line and the normal in the same square viewing window.
d.
Answer to Problem 9E
Explanation of Solution
Given information:
The function is
Graph:
Using graphing calculator:
Interpretation:
From the graph it is clear that all the curve passes through the point
Chapter 1 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