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 49E

a.

To determine

To graph the function using graphing device and find the maximum and minimum value of the function f.

Expert Solution

Explanation of Solution

Given information : Use graphing device to graph the function f(x)=x2+1.79x3.21 .

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 f(x)=x2+1.79x3.21 which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.1, Problem 49E

Interpretation :

From the above graph, it can be observed that the minimum value is at (4.01)

b.

To determine

To Find: The exact maximum or minimum value of the function f(x)=x2+1.79x3.21 and compare it with the above answer.

Expert Solution

Answer to Problem 49E

The value of minima is f(0.85)=(4.01)

Of course, the result agrees with what our graphing program gave us with the difference that the program rounded the answer to three decimal places.

Explanation of Solution

Given: The function is f(x)=x2+1.79x3.21

Calculation:

This is a quadratic function with a=1, and b=1.79 . Thus, the maximum or minimum value occurs at

  x=b2a=1.7921=1.792=0.895

Since, a>0 , the function has the minimum value

  f(0.895)=(0.895)2+1.79(0.895)3.21=4.011025

Of course, the result agrees with what our graphing program gave us with the difference that the program rounded the answer to three decimal places.

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