Concept explainers
a.
To fill in the gaps: with reference to the provided graph
a.
Answer to Problem 4E
A function value f ( a ) is a
Explanation of Solution
Given information: A function value f ( a ) is a local maximum value of f if f ( a ) is the ______ value of f on some interval containing a . From the graph of f , we see that one local maximum value of f is _____ and that this value occurs when x is ______.
Graph:
From the provided information, consider,
Interpretation:
Local maximum value of f ( a ) on a graph of f is the highest value on an interval containing a . Therefore, the local maximum value on the provided graph of f is 7, at x = 2.
Hence, a function value f ( a ) is a local maximum value of f if f ( a ) is the highest value of f on some interval containing a . From the graph of f , we see that one local maximum value of f is 7 and that this value occurs when x is 2 .
b.
To fill in the gaps: with reference to the provided graph
b.
Answer to Problem 4E
A function value f ( a ) is a
Explanation of Solution
Given information: A function value f ( a ) is a local minimum value of f if f ( a ) is the ______ value of f on some interval containing a . From the graph of f , we see that one local minimum value of f is _____ and that this value occurs when x is ______.
Graph:
From the provided information, consider,
Interpretation:
The local minimum value of f ( a ) on a graph of f is the lowest value on an interval containing a . The local minimum value on the provided graph is 2, at x = 4.
Hence, a function value f ( a ) is a local minimum value of f if f ( a ) is the lowest value of f on some interval containing a . From the graph of f , we see that one local minimum value of f is 2 and that this value occurs when x is 4 .
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition