shown in Figure 5.1.2, and that the pieces of f are either portions of lines or portions of circles. In addition, let F be an antiderivative of f and say that F(0) = -1. Finally, assume that for x ≤0 and x ≥ 7, f(x) = 0. y = f(x) An 2 3 4 5 1 -1 6 Figure 5.1.2. At left, the graph of y = f(x). a. On what interval(s) is F an increasing function? On what intervals is F decreasing? b. On what interval(s) is F concave up? concave down? neither? c. At what point(s) does F have a relative minimum? a relative maximum? d. Use the given information to determine the exact value of F(x) for 1, 2, ..., 7. In addition, what are the values of F(-1) and F(8)? x =
shown in Figure 5.1.2, and that the pieces of f are either portions of lines or portions of circles. In addition, let F be an antiderivative of f and say that F(0) = -1. Finally, assume that for x ≤0 and x ≥ 7, f(x) = 0. y = f(x) An 2 3 4 5 1 -1 6 Figure 5.1.2. At left, the graph of y = f(x). a. On what interval(s) is F an increasing function? On what intervals is F decreasing? b. On what interval(s) is F concave up? concave down? neither? c. At what point(s) does F have a relative minimum? a relative maximum? d. Use the given information to determine the exact value of F(x) for 1, 2, ..., 7. In addition, what are the values of F(-1) and F(8)? x =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Needed help with parts a through d only please. Thank you!
![Activity 5.1.2. Suppose that the function y = f(x) is given by the graph
shown in Figure 5.1.2, and that the pieces of f are either portions of lines or
portions of circles. In addition, let F be an antiderivative of f and say that
F(0) = -1. Finally, assume that for x ≤ 0 and x ≥ 7, ƒ(x) = 0.
1
-1+
y = f(x)
2
3
4
5
6
7
Figure 5.1.2. At left, the graph of y = f(x).
a. On what interval(s) is F an increasing function? On what intervals is F
decreasing?
b. On what interval(s) is F concave up? concave down? neither?
c. At what point(s) does F have a relative minimum? a relative maximum?
d. Use the given information to determine the exact value of F(x) for
x = 1, 2, ‚ 7. In addition, what are the values of F(−1) and F(8)?
..
"...
e. Based on your responses to all of the preceding questions, sketch a
complete and accurate graph of y = F(x) on the axes provided, being
sure to indicate the behavior of F for x < 0 and x > 7. Clearly indicate
the scale on the vertical and horizontal axes of your graph.
f. What happens if we change one key piece of information: in particular,
say that G is an antiderivative of ƒ and G(0) = 0. How (if at all) would
your answers to the preceding questions change? Sketch a graph of G on
the same axes as the graph of F you constructed in (e).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce3589f0-5608-4fb5-a11c-ce1805f2c8e6%2Fc3d69bde-d942-430e-bf33-9c85ace9c6f7%2F5jswlzr_processed.png&w=3840&q=75)
Transcribed Image Text:Activity 5.1.2. Suppose that the function y = f(x) is given by the graph
shown in Figure 5.1.2, and that the pieces of f are either portions of lines or
portions of circles. In addition, let F be an antiderivative of f and say that
F(0) = -1. Finally, assume that for x ≤ 0 and x ≥ 7, ƒ(x) = 0.
1
-1+
y = f(x)
2
3
4
5
6
7
Figure 5.1.2. At left, the graph of y = f(x).
a. On what interval(s) is F an increasing function? On what intervals is F
decreasing?
b. On what interval(s) is F concave up? concave down? neither?
c. At what point(s) does F have a relative minimum? a relative maximum?
d. Use the given information to determine the exact value of F(x) for
x = 1, 2, ‚ 7. In addition, what are the values of F(−1) and F(8)?
..
"...
e. Based on your responses to all of the preceding questions, sketch a
complete and accurate graph of y = F(x) on the axes provided, being
sure to indicate the behavior of F for x < 0 and x > 7. Clearly indicate
the scale on the vertical and horizontal axes of your graph.
f. What happens if we change one key piece of information: in particular,
say that G is an antiderivative of ƒ and G(0) = 0. How (if at all) would
your answers to the preceding questions change? Sketch a graph of G on
the same axes as the graph of F you constructed in (e).
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