Concept explainers
To fill in the blank in the statement “The ____ ____ to the graph of a function at a point is the line whose slope best approximates the slope of the graph at the point.”
Answer to Problem 2E
The tangent line to the graph of a function at a point is the line whose slope best approximates the slope of the graph at the point.
Explanation of Solution
Given:
The ____ ____ to the graph of a function at a point is the line whose slope best approximates the slope of the graph at the point.
To find the rate at which a graph rises or falls at a single point, we find the slope of the tangent line at that point. The tangent line to the graph of a function f at a point P (x1, y1) is the line whose slope is best approximates the slope of the graph at the point.
Therefore, the tangent line to the graph of a function at a point is the line whose slope best approximates the slope of the graph at the point.
Chapter 12 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