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Preview Activity 5.1.1. Suppose that the following information is known about a function f: the graph of its derivative, y = f'(x), is given in Figure 5.1.1 Further, assume that f' is piecewise linear (as pictured) and that for x ≤ 0 and x ≥ 6, ƒ'(x) = 0. Finally, it is given that ƒ(0) = 1.

Preview Activity 5.1.1. Suppose that the following information is known about a function f: the graph of its derivative, y = f'(x), is given in Figure 5.1.1 Further, assume that f' is piecewise linear (as pictured) and that for x ≤ 0 and x ≥ 6, ƒ'(x) = 0. Finally, it is given that ƒ(0) = 1.

Advanced Engineering Mathematics
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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Only need part f answered, please. Thank you!

 

Preview Activity 5.1.1. Suppose that the following information is known about a function ƒ: the graph of its derivative, y = f'(x), is given in Figure 5.1.1. Further, assume that ƒ' is piecewise linear (as pictured) and that for x ≤ 0 and | x ≥ 6, ƒ'(x) = 0. Finally, it is given that ƒ(0) = 1. - -1 -3- y = f'(x) 3 LO 5 3 -1 -3 3 5
Transcribed Image Text:Preview Activity 5.1.1. Suppose that the following information is known about a function ƒ: the graph of its derivative, y = f'(x), is given in Figure 5.1.1. Further, assume that ƒ' is piecewise linear (as pictured) and that for x ≤ 0 and | x ≥ 6, ƒ'(x) = 0. Finally, it is given that ƒ(0) = 1. - -1 -3- y = f'(x) 3 LO 5 3 -1 -3 3 5
Figure 5.1.1. At left, the graph of y = f'(x); at right, axes for plotting y = f(x). a. On what interval(s) is ƒ an increasing function? On what intervals is f decreasing? b. On what interval(s) is ƒ concave up? concave down? c. At what point(s) does f have a relative minimum? a relative maximum? d. Recall that the Total Change Theorem tells us that 1 ƒ(1) — ƒ(0) = √ ^ f'(x) dx. 0 What is the exact value of f(1)? e. Use the given information and similar reasoning to that in (d) to determine the exact value of f(2), ƒ(3), ƒ(4), ƒ(5), and ƒ(6). f. 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 > 6.
Transcribed Image Text:Figure 5.1.1. At left, the graph of y = f'(x); at right, axes for plotting y = f(x). a. On what interval(s) is ƒ an increasing function? On what intervals is f decreasing? b. On what interval(s) is ƒ concave up? concave down? c. At what point(s) does f have a relative minimum? a relative maximum? d. Recall that the Total Change Theorem tells us that 1 ƒ(1) — ƒ(0) = √ ^ f'(x) dx. 0 What is the exact value of f(1)? e. Use the given information and similar reasoning to that in (d) to determine the exact value of f(2), ƒ(3), ƒ(4), ƒ(5), and ƒ(6). f. 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 > 6.
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