Find the derivative of this function
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the derivative of this function but Do Not Simplify
![The given mathematical expression is:
\[ d) \quad R(x) = \frac{3x^4}{2x-1} \]
This is a rational function where:
- The numerator is \(3x^4\), which is a polynomial of degree 4.
- The denominator is \(2x-1\), which is a linear polynomial.
The function \(R(x)\) is defined for all values of \(x\) except where the denominator equals zero. This occurs at \(x = \frac{1}{2}\), creating a vertical asymptote at this point.
You can analyze this function to explore its behaviors, such as determining where it is increasing or decreasing, finding its intercepts, and analyzing its asymptotic behavior.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28b0c599-bbea-4dfa-aec4-e0091988eaa4%2Fad96f78c-c0ef-4b9f-868a-880d837c1ba4%2F0jyqa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The given mathematical expression is:
\[ d) \quad R(x) = \frac{3x^4}{2x-1} \]
This is a rational function where:
- The numerator is \(3x^4\), which is a polynomial of degree 4.
- The denominator is \(2x-1\), which is a linear polynomial.
The function \(R(x)\) is defined for all values of \(x\) except where the denominator equals zero. This occurs at \(x = \frac{1}{2}\), creating a vertical asymptote at this point.
You can analyze this function to explore its behaviors, such as determining where it is increasing or decreasing, finding its intercepts, and analyzing its asymptotic behavior.
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