BuyFind

Precalculus: Mathematics for Calcu...

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

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)=x58x3+20x and also the values of x on which it occurs.

Expert Solution

Answer to Problem 58E

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).

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.1, Problem 58E

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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