Chapter 5.3, Problem 55PPS

(a)

To determine

To Find: The table values to sketch the function.

Answer to Problem 55PPS

The required graph is shown in Figure 1

Explanation of Solution

Given:

The given equation for the model is $p\left(x\right)-x^4+40x^2-144$ .

Calculation:

Consider the given function is,

  $p\left(x\right)-x^4+40x^2-144$

Then, the table for the function is shown in Table 1

Table 1

$x$	$p\left(x\right)$
-7	-585
-6	0
-4	240
-3	135
-2	0
0	-144
1	-105
2	0
4	240
6	0
7	-585

The graph from the above table is shown in Figure 1

  

Figure 1

(b)

To determine

To Find: The zeroes of the function.

Answer to Problem 55PPS

The

Explanation of Solution

Consider the given equation,

  $p\left(x\right)-x^4+40x^2-144$

Solve the given equation as,

  $\begin{array}{l}-x^4+40x^2-144=0\\ \left(-x^2+4\right)\left(-x^2-36\right)=0\\ x=\pm 2,\pm 6\end{array}$

Thus, the required root is $x=-2,2,-6,6$ .

(c)

To determine

To Find: The two values between which the company sell in order to be profitable.

Answer to Problem 55PPS

Thus, the graph shows that the company earns profit between $x=2,6$ .

Explanation of Solution

Consider the graph of the function shown in Figure 1

The graph shows that the company earns profit between $x=2,6$ .

(d)

To determine

To Find: The reason why only two zeroes are considered in part (c).

Answer to Problem 55PPS

There are only two zeroes in part (c) as the items cannot be included in the negatives. The negative of the profit refer to the loss.

Explanation of Solution

There are only two zeroes in part (c) as the items cannot be included in the negatives. The negative of the profit refer to the loss.

Thus, the roots 2,6 are reasonable and $-2,-6$ .