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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![In the given image, we have the following mathematical expressions:
1. The function \( f(x) \) is defined as:
\[
f(x) = x^3
\]
2. The expression representing the difference quotient of the function \( f(x) \) is:
\[
\frac{f(x + \Delta x) - f(x)}{\Delta x}
\]
This setup is commonly used in calculus to find the derivative of a function. The difference quotient is a fundamental concept for understanding the derivative, representing the average rate of change of the function over an interval \(\Delta x\). As \(\Delta x\) approaches zero, the difference quotient approaches the derivative of the function at \(x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faac2a72d-7bfe-4f67-91ba-184dbded01e0%2F8f6a4322-4c8c-429e-882b-255f843653d3%2Fa1sjy1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In the given image, we have the following mathematical expressions:
1. The function \( f(x) \) is defined as:
\[
f(x) = x^3
\]
2. The expression representing the difference quotient of the function \( f(x) \) is:
\[
\frac{f(x + \Delta x) - f(x)}{\Delta x}
\]
This setup is commonly used in calculus to find the derivative of a function. The difference quotient is a fundamental concept for understanding the derivative, representing the average rate of change of the function over an interval \(\Delta x\). As \(\Delta x\) approaches zero, the difference quotient approaches the derivative of the function at \(x\).
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