a.
To find the slope of the line joining two points.
a.
Answer to Problem 6PS
Explanation of Solution
Given information:
One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point
Find the slope of the line joining
Here, we will consider a point
We will first differentiate the function
Now, the slope of the tangent line at point
As we know that, the slope of the line passing through the points
Hence, the slope of the line passing through the points
Hence, the slope of the tangent line at point
b.
To find the slope
b.
Answer to Problem 6PS
Explanation of Solution
Given information:
One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point
Find the slope
Calculation:
The slope of the line passing through the points
Hence, the slope of the tangent line at point
c.
To find the slope
c.
Answer to Problem 6PS
Explanation of Solution
Given information:
One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point
Find the slope
Calculation:
The slope of the line passing through the points
Hence, the slope of the tangent line at point
d.
To find the slope
d.
Answer to Problem 6PS
Explanation of Solution
Given information:
One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point
Find the slope
Calculation:
The slope of the line passing through the points
Hence, the slope
e.
To evaluate the slope formula.
e.
Answer to Problem 6PS
For
For
For
Explanation of Solution
Given information:
One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point
Evaluate the slope formula from part
Calculation:
For
For
For
Hence, the slope gives the same values as we get in parts
f.
To write the conclusion about the slope
f.
Answer to Problem 6PS
The slope of the tangent line at point
Explanation of Solution
Given information:
One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point
What can you conclude the slope
Calculation:
Now, from the slope formula
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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