1. The graph of f. the derivative of f, is shown for -2sxg5. On what intervals is f increasing? Justify your answer Graph of

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. The graph of f, the derivative of f, is shown for – 2sxs5. On what intervals is f
increasing? Justify your answer.
Graph of
2. The graph of f, the derivative of a function f is shown. At what value(s) of x does
f2) have a point of inflection? Justify your answer.
3. Find all values of x for which the function f defined by fx) = (x - 3)s * is increasing.
Justify your answer.
4. The polynomial function f has selected values of its second derivative " given in the
table. Which of the statements must be true?
(A) f is increasing on the interval (0, 2)
B)f has a local maximum at x =1
(Of has a point of inflection at x=1
* 0 12 3
0 -7 4
(D)f changes concavity in the interval (0, 2)
5. Find the absolute minimum value of g(x) = 4x +3x - 6x +1 on the closed interval
[-2, 1]
6. If f"(x) = x(x+1)x – 2), then the graph of f has inflection points when x =? Justify
your answer.
Transcribed Image Text:1. The graph of f, the derivative of f, is shown for – 2sxs5. On what intervals is f increasing? Justify your answer. Graph of 2. The graph of f, the derivative of a function f is shown. At what value(s) of x does f2) have a point of inflection? Justify your answer. 3. Find all values of x for which the function f defined by fx) = (x - 3)s * is increasing. Justify your answer. 4. The polynomial function f has selected values of its second derivative " given in the table. Which of the statements must be true? (A) f is increasing on the interval (0, 2) B)f has a local maximum at x =1 (Of has a point of inflection at x=1 * 0 12 3 0 -7 4 (D)f changes concavity in the interval (0, 2) 5. Find the absolute minimum value of g(x) = 4x +3x - 6x +1 on the closed interval [-2, 1] 6. If f"(x) = x(x+1)x – 2), then the graph of f has inflection points when x =? Justify your answer.
7. Let g be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real
numbers x, such that g(4) = 12 and g(5) = 18. Of the following, which is a possible value
for g(6)? Explain how you know.
(A) 15
(B) 18
(C) 21
(D) 24
(E) 27
8. The graph of flx) is shown. On the interval (F, G), which of the following is true?
fx) < 0
III. f"(x) < 0
I.
II f2) > 0
f(x)
H
(A) I only
(B) I and II only
(© I and III only
(D) I, II, and II
9. The graph of f"(x) is shown. For what value(s) of x does the graph of f have a point of
inflection? Justify your answers.
10. If f(1) = 3, (1) = 0, and f"(1) = - 3, does f(x) have a relative minimum or
maximum at x =1? Explain
Calculator:
11. At what x value(s) does the graph of the function y =x +6x + 7x- 2cosx change
concavity? Justify your answer.
Transcribed Image Text:7. Let g be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real numbers x, such that g(4) = 12 and g(5) = 18. Of the following, which is a possible value for g(6)? Explain how you know. (A) 15 (B) 18 (C) 21 (D) 24 (E) 27 8. The graph of flx) is shown. On the interval (F, G), which of the following is true? fx) < 0 III. f"(x) < 0 I. II f2) > 0 f(x) H (A) I only (B) I and II only (© I and III only (D) I, II, and II 9. The graph of f"(x) is shown. For what value(s) of x does the graph of f have a point of inflection? Justify your answers. 10. If f(1) = 3, (1) = 0, and f"(1) = - 3, does f(x) have a relative minimum or maximum at x =1? Explain Calculator: 11. At what x value(s) does the graph of the function y =x +6x + 7x- 2cosx change concavity? Justify your answer.
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