5 1 Let f(x)= = on the interval [1,4]. For a E (1,4), construct a rectangle from x = 1 to x = a with height f(a). (See various rectangles in Figure 1.) We want to determine a so that the rectangle constructed from 1 to x has a maximum area. (See Figure 2) 5 4 Figure 1 Figure 2 3 2 1 1.3 22.2 3 3.4 1 2 The area, as a function of x, is A = A(z) = And, A'(x) = To determine the value of x that yields a maximum area, solve A'(x) = 0. x= (4 5432 1 3 1+ Sign out
5 1 Let f(x)= = on the interval [1,4]. For a E (1,4), construct a rectangle from x = 1 to x = a with height f(a). (See various rectangles in Figure 1.) We want to determine a so that the rectangle constructed from 1 to x has a maximum area. (See Figure 2) 5 4 Figure 1 Figure 2 3 2 1 1.3 22.2 3 3.4 1 2 The area, as a function of x, is A = A(z) = And, A'(x) = To determine the value of x that yields a maximum area, solve A'(x) = 0. x= (4 5432 1 3 1+ Sign out
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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### Understanding Maximum Area of Rectangles under a Curve
#### Problem Statement
Given the function \( f(x) = \frac{5}{x^2} \) on the interval \([1,4]\),
1. For \( a \in (1, 4) \), construct a rectangle from \( x = 1 \) to \( x = a \) with height \( f(a) \). (See various rectangles in Figure 1.)
2. We want to determine \( x \) such that the rectangle constructed from 1 to \( x \) has a maximum area. (See Figure 2.)
#### Visual Representation
- **Figure 1**:
- This figure depicts the graph of the function \( f(x) = \frac{5}{x^2} \).
- It shows two rectangles under the curve:
- The first rectangle extends from \( x = 1 \) to \( x \approx 1.3 \) with height \( f(1.3) \).
- The second rectangle extends from \( x = 1 \) to \( x \approx 2.2 \) with height \( f(2.2) \).
- **Figure 2**:
- Similar to Figure 1, this figure shows the graph of \( f(x) = \frac{5}{x^2} \).
- It shows a rectangle extending from \( x = 1 \) to \( x \approx 3.4 \) with height \( f(3.4) \).
 (Please replace this text with an actual image if needed)
#### Mathematical Formulation
- The area, as a function of \( x \), is \( A = A(x) = \) [To be filled by the student].
- And, \( A'(x) = \) [To be filled by the student].
To determine the value of \( x \) that yields a maximum area, solve \( A'(x) = 0 \).
\[ x = \] [To be filled by the student].
---
This transcription provides a clean, educational explanation for understanding the problem visually and mathematically. Please replace placeholders with appropriate values if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2Fbfe39bf7-3fff-445d-867b-934667decb4d%2F500077q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Understanding Maximum Area of Rectangles under a Curve
#### Problem Statement
Given the function \( f(x) = \frac{5}{x^2} \) on the interval \([1,4]\),
1. For \( a \in (1, 4) \), construct a rectangle from \( x = 1 \) to \( x = a \) with height \( f(a) \). (See various rectangles in Figure 1.)
2. We want to determine \( x \) such that the rectangle constructed from 1 to \( x \) has a maximum area. (See Figure 2.)
#### Visual Representation
- **Figure 1**:
- This figure depicts the graph of the function \( f(x) = \frac{5}{x^2} \).
- It shows two rectangles under the curve:
- The first rectangle extends from \( x = 1 \) to \( x \approx 1.3 \) with height \( f(1.3) \).
- The second rectangle extends from \( x = 1 \) to \( x \approx 2.2 \) with height \( f(2.2) \).
- **Figure 2**:
- Similar to Figure 1, this figure shows the graph of \( f(x) = \frac{5}{x^2} \).
- It shows a rectangle extending from \( x = 1 \) to \( x \approx 3.4 \) with height \( f(3.4) \).
 (Please replace this text with an actual image if needed)
#### Mathematical Formulation
- The area, as a function of \( x \), is \( A = A(x) = \) [To be filled by the student].
- And, \( A'(x) = \) [To be filled by the student].
To determine the value of \( x \) that yields a maximum area, solve \( A'(x) = 0 \).
\[ x = \] [To be filled by the student].
---
This transcription provides a clean, educational explanation for understanding the problem visually and mathematically. Please replace placeholders with appropriate values if needed.
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