# To find all the local maximum and minimum value of the function and the value of x at which each occur using the graph of the function given.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.3, Problem 32E

a.

To determine

## To find all the local maximum and minimum value of the function and the value of x at which each occur using the graph of the function given.

Expert Solution

The local maximum and minimum value of the function are 2,1 and 1 respectively and the value of x at which each occur are 2,2 and 0 respectively.

### Explanation of Solution

Given information :

The graph of the function is given.

Draw a viewing rectangle on each of the extremum of the graph of the function which is provided in the question.

The graph is shown below:

From the above graph, it can be observed that the point (2,f(2)) and (2,f(2)) are the highest point on the graph of f within the viewing rectangle, so the number f(2)=2 and f(2)=1 are a local maximum value of the function.

Similarly, it can be observed that the point (0,f(0)) is the lowest points on the graph of f within the viewing rectangle, so the number f(0)=1 is the local minimum value of the function.

Hence,

The local maximum and minimum value of the function are 2,1 and 1 respectively and the value of x at which each occur are 2,2 and 0 respectively.

b.

To determine

### To find the interval on which the function is increasing and on which the function is decreasing.

Expert Solution

The function f is increasing on (,2] and [0,2] and decreasing on [2,0] and [2,) .

### Explanation of Solution

Given information :

The graph of the function is given.

Concept used:

The function is increasing on an interval I if f(x1)<f(x2) whenever x1<x2 in I .

The function is decreasing on an interval I if f(x1)>f(x2) whenever x1<x2 in I .

The graph of the function is shown below:

Use definition of increasing and decreasing function.

From the above graph, it can be observed that the function f is increasing on (,2] and [0,2] as f()=<f(2)=2 for <2 and f(0)=1<f(2)=1 for 0<2 respectively and decreasing on [2,0] and [2,) as f(2)=2>f(0)=1 for 2<0 and f(2)=1>f()= for 2< respectively.

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