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
![**Problem Statement:**
Find the second derivative of the function \(y = 4x + 9\) with respect to \(x\).
**Solution:**
1. **First Derivative:**
- Given \(y = 4x + 9\)
- Derivative of \(y\) with respect to \(x\), denoted as \(\frac{dy}{dx}\), is:
\[
\frac{dy}{dx} = 4
\]
2. **Second Derivative:**
- Derivative of \(\frac{dy}{dx} = 4\) with respect to \(x\):
\[
\frac{d^2y}{dx^2} = 0
\]
Since \(4\) is a constant, its derivative with respect to \(x\) is \(0\).
**Conclusion:**
The second derivative \(\frac{d^2y}{dx^2}\) is \(0\), indicating that the original function is linear and has no curvature.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F700fc622-904c-44c3-8a84-236b54db198f%2Ffb613b65-1588-4e72-9285-98b367676fcc%2F8j4n0i6_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the second derivative of the function \(y = 4x + 9\) with respect to \(x\).
**Solution:**
1. **First Derivative:**
- Given \(y = 4x + 9\)
- Derivative of \(y\) with respect to \(x\), denoted as \(\frac{dy}{dx}\), is:
\[
\frac{dy}{dx} = 4
\]
2. **Second Derivative:**
- Derivative of \(\frac{dy}{dx} = 4\) with respect to \(x\):
\[
\frac{d^2y}{dx^2} = 0
\]
Since \(4\) is a constant, its derivative with respect to \(x\) is \(0\).
**Conclusion:**
The second derivative \(\frac{d^2y}{dx^2}\) is \(0\), indicating that the original function is linear and has no curvature.
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