# The local maximum and minimum values of the function g ( x ) = x 5 − 8 x 3 + 20 x and also the values of x on which it occurs.

### 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 3.1, Problem 58E
To determine

## To find: The local maximum and minimum values of the function g(x)=x5−8x3+20x and also the values of x on which it occurs.

Expert Solution

The local maximum value of the function g(x)=x58x3+20x is equal to 7.866 at x=1.93 and 13.018 at x=1.036 and the local minimum value of the function g(x)=x58x3+20x is equal to 13.018 at x=1.036 and 7.866 at x=1.93 .

### Explanation of Solution

Given information:

The given function is g(x)=x58x3+20x .

Calculation:

Graph the given function g(x)=x58x3+20x .

To graph a function y=x58x3+20x , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press Y= key and enter right hand side of the equation y=x58x3+20x after the symbol Y1 . Enter the keystrokes X^58X^3+20X .

The display will show the equation,

Y1=X^58X^3+20X

Now, press the GRAPH key and TRACE key to produce the graph of given function in standard window as shown in Figure (1).

Figure (1)

As observed from the graph, the function has local maximum value equal to 7.866 at x=1.93 and 13.018 at x=1.036 .

As observed from the graph, the function has local minima value equal to 13.018 at x=1.036 and 7.866 at x=1.93 .

Therefore, the local maximum value of the function g(x)=x58x3+20x is equal to 7.866 at x=1.93 and 13.018 at x=1.036 and the local minimum value of the function g(x)=x58x3+20x is equal to 13.018 at x=1.036 and 7.866 at x=1.93 .

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