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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.3, Problem 4E

a.

To determine

**To fill in the gaps**: with reference to the provided graph

Expert Solution

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 __.

**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 determine

**To fill in the gaps**: with reference to the provided graph

Expert Solution

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 __.

**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 __.