Concept explainers
To Sketch: The given function with local and minimum extrema and
Given:
Graph:
Sketch the graph of
Find the extrema:
Find the first derivative of the function:
Find the second derivative of the function:
To find the
Factor the term:
Factor by grouping:
If any individual factor on the left side of the equation is equal to
Thus, the values of
Evaluate the second derivative at
Split
Substitute any number, such as
Replace the variable
Substitute any number, such as
Replace the variable
Since the first derivative changed signs from negative to positive around
Since the first derivative did not change signs around
Find the value of
Substitute
The function
Find the zeroes of the function
The function has zeros at
Thus, the function
End behaviour:
Use the limits to describe its end behaviour.
The graph rises to the left and rises to the right
Chapter 2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- 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