College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 28P
Related questions
Question
![### Problem 2. Absolute Maximum and Minimum Values
Find the absolute maximum and absolute minimum values of the function
\[ f(x) = x + \frac{4}{x}, \quad x \in \left[\frac{1}{5}, 16 \right]. \]
**Explanation:**
We are given a function \( f(x) \) defined as \( f(x) = x + \frac{4}{x} \) and we need to determine its absolute maximum and minimum values within the closed interval \( \left[\frac{1}{5}, 16 \right] \). This involves calculating the values of the function at the critical points within the interval and at the endpoints of the interval.
To solve this, we will:
1. Find the derivative \( f'(x) \) to locate critical points.
2. Evaluate \( f(x) \) at the critical points and at the boundaries \( x = \frac{1}{5} \) and \( x = 16 \).
3. Compare these values to determine the absolute maximum and minimum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4526b347-f4c2-4959-b519-c79fc40f5b52%2F3ff5af0f-4160-43f7-962e-64995c566560%2F31o5iuj_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 2. Absolute Maximum and Minimum Values
Find the absolute maximum and absolute minimum values of the function
\[ f(x) = x + \frac{4}{x}, \quad x \in \left[\frac{1}{5}, 16 \right]. \]
**Explanation:**
We are given a function \( f(x) \) defined as \( f(x) = x + \frac{4}{x} \) and we need to determine its absolute maximum and minimum values within the closed interval \( \left[\frac{1}{5}, 16 \right] \). This involves calculating the values of the function at the critical points within the interval and at the endpoints of the interval.
To solve this, we will:
1. Find the derivative \( f'(x) \) to locate critical points.
2. Evaluate \( f(x) \) at the critical points and at the boundaries \( x = \frac{1}{5} \) and \( x = 16 \).
3. Compare these values to determine the absolute maximum and minimum.
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