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...
Related questions
Question
A. Find all values of x in the domain F such that F’(x) does not exist.
B.Find the critical numbers of the function
![Certainly! Here is the transcription and explanation suitable for an educational website.
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**Transcription of Mathematical Notation:**
The function \( f(x) \) is defined as:
\[ f(x) = x^{4/5} (x - 8)^2 \]
**Explanation:**
The given function, \( f(x) = x^{4/5} (x - 8)^2 \), is a mathematical expression consisting of a product of two terms.
1. **First Term: \( x^{4/5} \)**
- This term involves the base \( x \) raised to the power of \( 4/5 \). This represents \( x \) raised to a fractional exponent, suggesting a root and a power. Specifically, it indicates the fifth root of \( x^4 \).
2. **Second Term: \( (x - 8)^2 \)**
- The second term is a binomial square. \( (x - 8)^2 \) means that \( x - 8 \) is multiplied by itself.
Together, this function combines a fractional exponent and a squared term, which can influence the shape and behavior of the function's graph.
In general, functions of this form may exhibit interesting characteristics such as changes in curvature, and points of inflection, and are useful in advanced calculus and algebra studies.
---
This transcription and explanation should help students and educators understand the mathematical notation and its implications in the context of higher mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24fae4ed-b1b1-4171-bba8-4d29349ae5e5%2F1ae7eae5-8c9d-4f8a-aea6-a13783975f67%2Flpn6ooo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here is the transcription and explanation suitable for an educational website.
---
**Transcription of Mathematical Notation:**
The function \( f(x) \) is defined as:
\[ f(x) = x^{4/5} (x - 8)^2 \]
**Explanation:**
The given function, \( f(x) = x^{4/5} (x - 8)^2 \), is a mathematical expression consisting of a product of two terms.
1. **First Term: \( x^{4/5} \)**
- This term involves the base \( x \) raised to the power of \( 4/5 \). This represents \( x \) raised to a fractional exponent, suggesting a root and a power. Specifically, it indicates the fifth root of \( x^4 \).
2. **Second Term: \( (x - 8)^2 \)**
- The second term is a binomial square. \( (x - 8)^2 \) means that \( x - 8 \) is multiplied by itself.
Together, this function combines a fractional exponent and a squared term, which can influence the shape and behavior of the function's graph.
In general, functions of this form may exhibit interesting characteristics such as changes in curvature, and points of inflection, and are useful in advanced calculus and algebra studies.
---
This transcription and explanation should help students and educators understand the mathematical notation and its implications in the context of higher mathematics.
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