A friend from New York City called me asking for help with a problem he was given. He needed to find the two horizontal tangents of the graph of the function f(x) = 2x³ + 6x² - 144x + 1 Please provide a detailed step by step description of how can we solve this problem, so that we can help my friend from New York City. Do not forget to submit your final answer into the answer boxes below and to upload a file with your explanation using the "Add Work" box. What is the negative value of where a horizontal tangent occurs? What is the positive value of a where a horizontal tangent occurs?
A friend from New York City called me asking for help with a problem he was given. He needed to find the two horizontal tangents of the graph of the function f(x) = 2x³ + 6x² - 144x + 1 Please provide a detailed step by step description of how can we solve this problem, so that we can help my friend from New York City. Do not forget to submit your final answer into the answer boxes below and to upload a file with your explanation using the "Add Work" box. What is the negative value of where a horizontal tangent occurs? What is the positive value of a where a horizontal tangent occurs?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Problem Statement:**
A friend from New York City called me asking for help with a problem he was given. He needed to find the two horizontal tangents of the graph of the function:
\[ f(x) = 2x^3 + 6x^2 - 144x + 1 \]
**Instructions:**
Please provide a detailed step-by-step description of how we can solve this problem, so that we can help my friend from New York City.
Do not forget to submit your final answer into the answer boxes below and to upload a file with your explanation using the "Add Work" box.
**Questions:**
- What is the negative value of \( x \) where a horizontal tangent occurs?
- [Enter answer here]
- What is the positive value of \( x \) where a horizontal tangent occurs?
- [Enter answer here]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca9cc0da-3805-4def-94c5-2b93bf19b878%2Fa62001c8-db0e-431e-bcf8-e7b8f7dbce11%2Femwvp_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A friend from New York City called me asking for help with a problem he was given. He needed to find the two horizontal tangents of the graph of the function:
\[ f(x) = 2x^3 + 6x^2 - 144x + 1 \]
**Instructions:**
Please provide a detailed step-by-step description of how we can solve this problem, so that we can help my friend from New York City.
Do not forget to submit your final answer into the answer boxes below and to upload a file with your explanation using the "Add Work" box.
**Questions:**
- What is the negative value of \( x \) where a horizontal tangent occurs?
- [Enter answer here]
- What is the positive value of \( x \) where a horizontal tangent occurs?
- [Enter answer here]
Expert Solution
Step 1
Let f(x) be the function then the slope of the tangent line is determined by f'(x).
A horizontal tangent means the tangent parallel to the x-axis.
A vertical tangent means the tangent line is parallel to y-axis.
To determine the horizontal tangent of the curve means the slope must be zero.
To determine the vertical tangent of the curve means the slope must be infinity.
Step by step
Solved in 2 steps
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