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.

Explanation of Solution

Given information : Use graphing device to graph the function $f\left(x\right)=x^2+1.79x-3.21$ .

Graph : Sketch the graph using graphing utility.

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

Step 2: Press $\boxed{\text{Y=}}$ button.

Step 3: Enter the expression $f\left(x\right)=x^2+1.79x-3.21$ which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  

Interpretation :

From the above graph, it can be observed that the minimum value is at $\left(-4.01\right)$

b.

To determine

To Find: The exact maximum or minimum value of the function $f\left(x\right)=x^2+1.79x-3.21$ and compare it with the above answer.

Answer to Problem 49E

The value of minima is $f\left(-0.85\right)=\left(-4.01\right)$

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 $f\left(x\right)=x^2+1.79x-3.21$

Calculation:

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

  $x=-\frac{b}{2a}=-\frac{1.79}{2\cdot 1}=-\frac{1.79}{2}=-0.895$

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

  $f\left(-0.895\right)={\left(-0.895\right)}^2+1.79\left(-0.895\right)-3.21=-4.011025$

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.