# To find the local maximum and local minimum of the function

### 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 36E

a.

To determine

## To find the local maximum and local minimum of the function

Expert Solution

### Explanation of Solution

Given information : the function is f(x)=3+x+x2x3 .

Graph : Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press Y= button.

Step 3: Enter the expression 3+x+x2x3 which is required to graph.

Step 4: Press GRAPH button to graph the function.

Step 5: Using TRACE feature on the calculator

The graph is obtained as:

From the above graph, it can be observed that the local maximum 4 when x1 and the local minimum 2.82 when x0.34

b.

To determine

### To find the interval on which the function is increasing and on which the function is decreasing up to two decimal

Expert Solution

The function f is decreasing on (0.34,1) and increasing on (,0.34)(1,) .

### Explanation of Solution

Given information :

The function is f(x)=3+x+x2x3 .

The graph of the function is obtained as:

Using TRACE feature on the calculator,

From the above graph, it can be observed that the function f is decreasing on (0.34,1) and increasing on (,0.34)(1,)

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