For all of the problems below, the function y = h(x) is given by the graph: 2 A -2 0 -2 2 1. What is the average value of h(x) on the interval [-4,4]? Why? 2. Let H be an antiderivative of h such that H(0) = 0. (a) On what intervals is H increasing/decreasing? Why? (b) On what intervals is H concave up/concave down? Why? (c) Determine the exact values H(-4), H(−2), H(0), H(2), H(4). (d) Based on your responses to the preceding questions, sketch a complete and accurate graph of y =H(x). For your graph, you may use the axes below or draw your own. Either way, clearly label each axis with the appropriate scale.
For all of the problems below, the function y = h(x) is given by the graph: 2 A -2 0 -2 2 1. What is the average value of h(x) on the interval [-4,4]? Why? 2. Let H be an antiderivative of h such that H(0) = 0. (a) On what intervals is H increasing/decreasing? Why? (b) On what intervals is H concave up/concave down? Why? (c) Determine the exact values H(-4), H(−2), H(0), H(2), H(4). (d) Based on your responses to the preceding questions, sketch a complete and accurate graph of y =H(x). For your graph, you may use the axes below or draw your own. Either way, clearly label each axis with the appropriate scale.
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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![For all of the problems below, the function y = h(x) is given by the graph:
2
A
-2
0
-2
2
1. What is the average value of h(x) on the interval [-4,4]? Why?
2. Let H be an antiderivative of h such that H(0) = 0.
(a) On what intervals is H increasing/decreasing? Why?
(b) On what intervals is H concave up/concave down? Why?
(c) Determine the exact values H(-4), H(−2), H(0), H(2), H(4).
(d) Based on your responses to the preceding questions, sketch a complete and accurate
graph of y =H(x). For your graph, you may use the axes below or draw your own.
Either way, clearly label each axis with the appropriate scale.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f81530b-e26c-4ea1-bd27-9f49a030a286%2F40fd131f-d547-44da-b961-70e89df979b7%2F6l7yly_processed.png&w=3840&q=75)
Transcribed Image Text:For all of the problems below, the function y = h(x) is given by the graph:
2
A
-2
0
-2
2
1. What is the average value of h(x) on the interval [-4,4]? Why?
2. Let H be an antiderivative of h such that H(0) = 0.
(a) On what intervals is H increasing/decreasing? Why?
(b) On what intervals is H concave up/concave down? Why?
(c) Determine the exact values H(-4), H(−2), H(0), H(2), H(4).
(d) Based on your responses to the preceding questions, sketch a complete and accurate
graph of y =H(x). For your graph, you may use the axes below or draw your own.
Either way, clearly label each axis with the appropriate scale.
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