To find: The first and second derivative of the function
Answer to Problem 46E
The first and second derivatives are,
Explanation of Solution
Given:
The function is,
Formula used:
The derivative of a function f , denoted by
Calculation:
Obtain the first derivative of the function
Compute
Simplify the numerator and obtain the derivative of the function,
Since the limit h approaches zero but is not equal to zero, cancel the common term h from both the numerator and the denominator,
Thus, the first derivative of the function is,
Obtain the second derivative of the function
Compute
Simplify the numerator,
Since the limit h approaches zero but is not equal to zero, cancel the common term h from both the numerator and the denominator,
Thus, the second derivative of the function is,
Therefore, the first and second derivatives of the functions are,
Use the online graphing calculator to draw the graph of the functions
From Figure 1, it is observed that the graph of
Take several points on the domain and estimate the slope of the function
For example, take the point 1 and the value of the slope of the tangent to the function
Thus, the derivative
Take several points on the domain and estimate the slope of tangent to the function
For example take the point 2 and the value of the slope of the tangent to the function
Thus, the derivative
Chapter 2 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