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
Graph the following, then find the real zeros of f and their multiplicities. State whether the graph of f crosses or touches the x-axis of each zero(show your work)
![The function given is:
\[ f(x) = x^2 (x^2 - 9)(3x + 5)^3 \]
This expression represents a polynomial function composed of multiple factors:
1. **\(x^2\)**: This is a basic quadratic expression featuring a power of two on the variable \(x\).
2. **\((x^2 - 9)\)**: This is a quadratic expression that can be factored further into \((x + 3)(x - 3)\) using the difference of squares formula.
3. **\((3x + 5)^3\)**: This indicates a cubic expression where the linear term \(3x + 5\) is raised to the third power, suggesting a triple root.
Each factor contributes to the overall shape and behavior of the function, including its roots, and influences its derivatives and integrals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcea6d79-c0c2-49cd-aa31-c3eca199518f%2F2ecba271-8c71-4ff8-97f7-25895c290d4e%2Ffvrcpfd_processed.png&w=3840&q=75)
Transcribed Image Text:The function given is:
\[ f(x) = x^2 (x^2 - 9)(3x + 5)^3 \]
This expression represents a polynomial function composed of multiple factors:
1. **\(x^2\)**: This is a basic quadratic expression featuring a power of two on the variable \(x\).
2. **\((x^2 - 9)\)**: This is a quadratic expression that can be factored further into \((x + 3)(x - 3)\) using the difference of squares formula.
3. **\((3x + 5)^3\)**: This indicates a cubic expression where the linear term \(3x + 5\) is raised to the third power, suggesting a triple root.
Each factor contributes to the overall shape and behavior of the function, including its roots, and influences its derivatives and integrals.
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