Chapter 6.4, Problem 13CYU

(a)

To determine

To graph:For the given function.

Explanation of Solution

Given information:

The given equation is $f\left(x\right)=0\cdot 48x^4-9\cdot 6x^3+53x^2-49x+599$ .

Graph:

Using MAPLE to graph the given function using the range $0\le x\le 10$ , as shown in figure (1).

  

Figure (1)

Interpretation:Graph for the function $f\left(x\right)=0\cdot 48x^4-9\cdot 6x^3+53x^2-49x+599$ is shown in figure (1).

(b)

To determine

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

Answer to Problem 13CYU

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 $f\left(x\right)=0\cdot 48x^4-9\cdot 6x^3+53x^2-49x+599$ .

Calculation:

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

Using the equation.

  $f\left(x\right)=x^3-5x^2+3x+1$

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

(c)

To determine

To graph:For the given function for $0\le x\le 12$ .

Explanation of Solution

Given information:

The given equation is $f\left(x\right)=0\cdot 48x^4-9\cdot 6x^3+53x^2-49x+599$ .

Graph:

Using MAPLE to graph the given function using the range $0\le x\le 12$ , as shown in figure (1).

  

Figure (1)

There is increase in sales.

Interpretation:Graph for the function $f\left(x\right)=0\cdot 48x^4-9\cdot 6x^3+53x^2-49x+599$ is shown in figure (1).

(d)

To determine

To find:Whether the trend will continue indefinitely.

Answer to Problem 13CYU

The function seems to be accurate till $2005$ only.

Explanation of Solution

Given information:

The given equation is $f\left(x\right)=0\cdot 48x^4-9\cdot 6x^3+53x^2-49x+599$ .

Calculation:

As there are many other form of media in the market today. CD will not increase any more. That means the sales of CD will not increase any more. That means the sales of the CD will decrease.

Therefore, the function seems to be accurate till $2005$ only.