Only need part f answered, please. Thank you! Preview Activity 5.1.1. Suppose that the following information is knownabout 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)3LO53-1-335 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 fdecreasing?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 that1ƒ(1) — ƒ(0) = √ ^ f'(x) dx.0What is the exact value of f(1)?e. Use the given information and similar reasoning to that in (d) todetermine 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 acomplete and accurate graph of y = f(x) on the axes provided, beingsure to indicate the behavior of f for x < 0 and x > 6.

Answered: Image /qna-images/answer/52169df8-4dde-4943-b6e9-e8a00ef89ccf.jpg

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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Question

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

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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