Chapter 6.4, Problem 22PPS

(a)

To determine

To graph:For the given function.

Explanation of Solution

Given information:

The given equation is $f\left(x\right)=0\cdot 0007x^3-0\cdot 014x^2+0\cdot 08x+0\cdot 96$ .

Graph:

Using MAPLE to graph the given function using the range $0\le x\le 30$ , as shown in figure (1).

  

Figure (1)

Interpretation:Graph for the function $f\left(x\right)=0\cdot 0007x^3-0\cdot 014x^2+0\cdot 08x+0\cdot 96$ is shown in figure (1).

(b)

To determine

To find: The turning points of the graph and its behavior.

Answer to Problem 22PPS

The relative minima is $x\approx 9\cdot 5$ and relative maxima is $x\approx 5$ .

Explanation of Solution

Given information:

The given equation is $f\left(x\right)=0\cdot 0007x^3-0\cdot 014x^2+0\cdot 08x+0\cdot 96$ .

Calculation:

Use the graphing calculator $\text{Ti}-83$ to find the relative maxima and minima as.

Using the equation.

  $f\left(x\right)=0\cdot 0007x^3-0\cdot 014x^2+0\cdot 08x+0\cdot 96$

Use the graphing calculator $\text{Ti}-83$ to find the relative maxima and minima as.

  

Press the shift and trace button to open the CALC option.

  

Go to minima option and set the left bound and the right bound.

  

Similarly, the relative maxima will be.

  

Therefore, the relative minima is $x\approx 9\cdot 1$ and relative maxima is $x\approx 4\cdot 1$ .

(c)

To determine

To find: The trends in gasoline price does the graph suggest.

Answer to Problem 22PPS

The price are increasing regularly.

Explanation of Solution

Given information:

The given equation is $f\left(x\right)=0\cdot 0007x^3-0\cdot 014x^2+0\cdot 08x+0\cdot 96$ .

Calculation:

There is drastic increase in the trend of the gasoline prices. The curve of the graph is constantly increasing. So, the prices are increasing regularly.

Therefore, the prices are increasing regularly.

(d)

To determine

To find:Whether the trend will continue indefinitely.

Answer to Problem 22PPS

The graph is increasing continuously.

Explanation of Solution

Given information:

The given equation is $f\left(x\right)=0\cdot 0007x^3-0\cdot 014x^2+0\cdot 08x+0\cdot 96$ .

Calculation:

Yes, it is reasonable to tell that the trend will increases indefinitely, as the graph is increasing continuously.

Therefore, the graph is increasing continuously.