Find the equation(s) of the tangent line(s) to the graph of the curve y-x-12x through the point (1, -12) not or the greph. (Enter your answers as a comma-separated list of equations.) Need Help? Read Vw Sand Work Beat to London Submit Answer
Find the equation(s) of the tangent line(s) to the graph of the curve y-x-12x through the point (1, -12) not or the greph. (Enter your answers as a comma-separated list of equations.) Need Help? Read Vw Sand Work Beat to London Submit Answer
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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Question
Find the equation(s) of the tangent line(s) to the graph of the curve
y = x3 − 12x
through the point
(1, −12)
not on the graph. (Enter your answers as a comma-separated list of equations.)
Find the equation(s) of the tangent line(s) to the graph of the curve
y = x3 − 12x
through the point
(1, −12)
not on the graph. (Enter your answers as a comma-separated list of equations.)
![**Tangent Lines Calculations**
To find the equation(s) of the tangent line(s) to the graph of the curve \(y = x^3 - 12x\) through the point \((1, -12)\) not on the graph, follow the steps below. Enter your answers as a comma-separated list of equations.
**Given Information:**
\[ y = x^3 - 12x \]
**Through Point:**
\[ (1, -12) \]
**Equations and Graphs:**
1. **Equation:**
\[
y - 0 = 8(x - 0) \quad \text{and} \quad y = 5(x - 2)
\]
2. **Calculated Tangent Lines:**
- \[
y = 8x
\]
- \[
3x = 0
\]
**Verification:**
\[
8x + y = 0 \quad \text{and} \quad 8y = -8x + 12 = 0
\]
**Second Tangent Line:**
\[
\frac {619}{2} y + \frac {5}{2} x = \frac {y}{4}
\]
- \[
8x = y = 0
\]
- \[
0
\]
- \[
5x + 4y + 27 = 0
\]
**Interactive Options Provided:**
- **Check Score:** Allows checking the current score.
- **Show Answer:** Reveals the correct answers.
- **Hide Solution:** Hides the detailed solution.
- **Try Another:** Generates a new problem to attempt.
**Instructions for Students:**
- To find the tangent lines, differentiate the given curve to find the slopes at the specified points.
- Then, use the point-slope form to write the equations of the tangent lines.
**Support Resources:**
- Click on **"Need Help?"** for further assistance.
- Use **"View Past Work (Saved Solution & Feedback)"** for reviewing previous attempts.
**Submission Panel:**
- After calculating your solutions, enter them in the provided field and click **"Submit Answer."**
- Students can also save their progress using the **"Save Assignment Progress"** option.
- Submit the completed assignment using the **"Submit Assignment"** button.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccaa2380-b7ef-4e35-b03b-57c3118a9f62%2F54045396-9259-4e52-8fa8-f18309882b81%2Fvuf8sc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Tangent Lines Calculations**
To find the equation(s) of the tangent line(s) to the graph of the curve \(y = x^3 - 12x\) through the point \((1, -12)\) not on the graph, follow the steps below. Enter your answers as a comma-separated list of equations.
**Given Information:**
\[ y = x^3 - 12x \]
**Through Point:**
\[ (1, -12) \]
**Equations and Graphs:**
1. **Equation:**
\[
y - 0 = 8(x - 0) \quad \text{and} \quad y = 5(x - 2)
\]
2. **Calculated Tangent Lines:**
- \[
y = 8x
\]
- \[
3x = 0
\]
**Verification:**
\[
8x + y = 0 \quad \text{and} \quad 8y = -8x + 12 = 0
\]
**Second Tangent Line:**
\[
\frac {619}{2} y + \frac {5}{2} x = \frac {y}{4}
\]
- \[
8x = y = 0
\]
- \[
0
\]
- \[
5x + 4y + 27 = 0
\]
**Interactive Options Provided:**
- **Check Score:** Allows checking the current score.
- **Show Answer:** Reveals the correct answers.
- **Hide Solution:** Hides the detailed solution.
- **Try Another:** Generates a new problem to attempt.
**Instructions for Students:**
- To find the tangent lines, differentiate the given curve to find the slopes at the specified points.
- Then, use the point-slope form to write the equations of the tangent lines.
**Support Resources:**
- Click on **"Need Help?"** for further assistance.
- Use **"View Past Work (Saved Solution & Feedback)"** for reviewing previous attempts.
**Submission Panel:**
- After calculating your solutions, enter them in the provided field and click **"Submit Answer."**
- Students can also save their progress using the **"Save Assignment Progress"** option.
- Submit the completed assignment using the **"Submit Assignment"** button.
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