Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Stock Value Analysis
#### Problem Statement
The price of Tommy Hilfiger stock during a 4-hour period is given below. If a third-degree polynomial models this stock, do you expect the stock to go up or down in the fifth period?
#### Data Representation
The table below shows the price of Tommy Hilfiger stock over a 4-hour period:
<table>
<thead>
<tr>
<th>Period Watching Stock Market</th>
<th>Price</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>$15.10</td>
</tr>
<tr>
<td>2</td>
<td>$14.76</td>
</tr>
<tr>
<td>3</td>
<td>$15.50</td>
</tr>
<tr>
<td>4</td>
<td>$14.85</td>
</tr>
</tbody>
</table>
### Analysis and Considerations
To determine whether the stock price will go up or down in the fifth period using a third-degree polynomial model, we need to consider the trend displayed by the given data points.
#### Approach:
1. **Plot the Data and Fit a Polynomial:**
Fit a third-degree polynomial to the data points. The general form of a third-degree polynomial is:
\[
P(x) = ax^3 + bx^2 + cx + d
\]
2. **Examine the Polynomial:**
By fitting the polynomial to the data points for periods 1 to 4, we can evaluate the polynomial at \( x = 5 \) to predict the stock price in the fifth period.
3. **Trend Analysis:**
Observe the polynomial's behavior around the previous data points to infer the trend and assess if the general direction is increasing or decreasing.
#### Conclusion
By following this approach, we can predict if the Tommy Hilfiger stock price will go up or down in the fifth period using third-degree polynomial modeling techniques.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F180e35fb-9b09-4fc5-8a6a-511bee286828%2F65cc56c2-2038-4c71-8384-14bcd2ba7762%2F8ug6g0e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Stock Value Analysis
#### Problem Statement
The price of Tommy Hilfiger stock during a 4-hour period is given below. If a third-degree polynomial models this stock, do you expect the stock to go up or down in the fifth period?
#### Data Representation
The table below shows the price of Tommy Hilfiger stock over a 4-hour period:
<table>
<thead>
<tr>
<th>Period Watching Stock Market</th>
<th>Price</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>$15.10</td>
</tr>
<tr>
<td>2</td>
<td>$14.76</td>
</tr>
<tr>
<td>3</td>
<td>$15.50</td>
</tr>
<tr>
<td>4</td>
<td>$14.85</td>
</tr>
</tbody>
</table>
### Analysis and Considerations
To determine whether the stock price will go up or down in the fifth period using a third-degree polynomial model, we need to consider the trend displayed by the given data points.
#### Approach:
1. **Plot the Data and Fit a Polynomial:**
Fit a third-degree polynomial to the data points. The general form of a third-degree polynomial is:
\[
P(x) = ax^3 + bx^2 + cx + d
\]
2. **Examine the Polynomial:**
By fitting the polynomial to the data points for periods 1 to 4, we can evaluate the polynomial at \( x = 5 \) to predict the stock price in the fifth period.
3. **Trend Analysis:**
Observe the polynomial's behavior around the previous data points to infer the trend and assess if the general direction is increasing or decreasing.
#### Conclusion
By following this approach, we can predict if the Tommy Hilfiger stock price will go up or down in the fifth period using third-degree polynomial modeling techniques.
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