8 Let f(x) = 2 on the interval [1, 4]. For a € (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 x so that the rectangle constructed from 1 to x has a maximum area. (See Figure 2) 8 7 6 5 4 3 2 1 I 1 1.3 X = Figure 1 2 2.2 3 3.4 The area, as a function of x, is A = A(x) = 8 7 6 5 4 3 2 1 And, A'(x) = To determine the value of that yields a maximum area, solve A'(x) = 0. Figure 2 x 2 3
8 Let f(x) = 2 on the interval [1, 4]. For a € (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 x so that the rectangle constructed from 1 to x has a maximum area. (See Figure 2) 8 7 6 5 4 3 2 1 I 1 1.3 X = Figure 1 2 2.2 3 3.4 The area, as a function of x, is A = A(x) = 8 7 6 5 4 3 2 1 And, A'(x) = To determine the value of that yields a maximum area, solve A'(x) = 0. Figure 2 x 2 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Let f(x)
8
7
6
5
4
=
For a € (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 x so that the rectangle constructed from 1 to x has a maximum area. (See Figure 2)
3
2
1
8
x²
on the interval [1, 4].
1 1.3
Figure 1
2 2.2
3 3.4
The area, as a function of ï, is A = A(x) =
=
8
7
6
5
4
3
2
1
Figure 2
X 2
And, A'(x) =
To determine the value of x that yields a maximum area, solve A'(x) = 0.
x =
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec27bc4f-e154-4e19-9e13-c5693df2d140%2Fe376875d-50da-4e8f-8ea2-7103c893cac5%2F54zo1k_processed.png&w=3840&q=75)
Transcribed Image Text:Let f(x)
8
7
6
5
4
=
For a € (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 x so that the rectangle constructed from 1 to x has a maximum area. (See Figure 2)
3
2
1
8
x²
on the interval [1, 4].
1 1.3
Figure 1
2 2.2
3 3.4
The area, as a function of ï, is A = A(x) =
=
8
7
6
5
4
3
2
1
Figure 2
X 2
And, A'(x) =
To determine the value of x that yields a maximum area, solve A'(x) = 0.
x =
3
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