* The following statement will be used for Problems 2-5 * A UCF mathematics Professor sampled a function f(x) which models a parameter in a physical system. The table below gives the values sampled of f(x) and its derivatives. It is assumed that both f(x) and f'(x) are defined and differentiable for all x. 0. 3. f (x) f'(x) f"(x) 1-1 -3-1-1 0. 0. 4 3 -2 -1 3 Table 1: Sampled values of f(x) and its derivatives Problem 2. Based on Table 1, select the statement that must be true: (A) There exists a point p E (0, 1) such that f (p) = -1. (B))f has at least 4 critical points in (0,5). (C) The equation f(x) - 5 has a solution in [0, 5]. (D) The function f has an inftection point between 4 and 5. (E) There exists a point q E (0,5) such that the slope of the tangent line to the graph of f at (q, f(q)) is 4. 47 니S 2- 4.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.2: Polynomial Functions
Problem 96E: What is the purpose of the Intermediate Value Theorem?
Question
* The following statement will be used for Problems 2-5 *
A UCF mathematics Professor sampled a function f(x) which models a parameter in a
physical system. The table below gives the values sampled of f(x) and its derivatives. It is
assumed that both f(x) and f'(x) are defined and differentiable for all x.
0.
3.
f (x)
f'(x)
f"(x)
1-1
-3-1-1
0.
0.
4
3 -2
-1
3
Table 1: Sampled values of f(x) and its derivatives
Problem 2. Based on Table 1, select the statement that must be true:
(A) There exists a point p E (0, 1) such that f (p) = -1.
(B))f has at least 4 critical points in (0,5).
(C) The equation f(x) - 5 has a solution in [0, 5].
(D) The function f has an inftection point between 4 and 5.
(E) There exists a point q E (0,5) such that the slope of the tangent line to the graph of
f at (q, f(q)) is 4.
47
니S
2-
4.
Transcribed Image Text:* The following statement will be used for Problems 2-5 * A UCF mathematics Professor sampled a function f(x) which models a parameter in a physical system. The table below gives the values sampled of f(x) and its derivatives. It is assumed that both f(x) and f'(x) are defined and differentiable for all x. 0. 3. f (x) f'(x) f"(x) 1-1 -3-1-1 0. 0. 4 3 -2 -1 3 Table 1: Sampled values of f(x) and its derivatives Problem 2. Based on Table 1, select the statement that must be true: (A) There exists a point p E (0, 1) such that f (p) = -1. (B))f has at least 4 critical points in (0,5). (C) The equation f(x) - 5 has a solution in [0, 5]. (D) The function f has an inftection point between 4 and 5. (E) There exists a point q E (0,5) such that the slope of the tangent line to the graph of f at (q, f(q)) is 4. 47 니S 2- 4.
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