150 100- 50 -5 - 50 -100 -150 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.) Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) Identify x-values where f"(x) is decreasing. (Enter your answer using interval notation.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
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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Consider the following.
f(x) = x3 - 6x2 + 8
(a) Find f'(x) and f"(x).
f'(x) = 3x2 – 12x
f"(x) = 6x – 12
(b) Graph f(x), f'(x), and f"(x) with a graphing utility.
y
y
y
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150F
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50
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-5
-5
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- 50-
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Transcribed Image Text:Consider the following. f(x) = x3 - 6x2 + 8 (a) Find f'(x) and f"(x). f'(x) = 3x2 – 12x f"(x) = 6x – 12 (b) Graph f(x), f'(x), and f"(x) with a graphing utility. y y y 150F 150F 150- 100 100 100 50 50 50 -5 -5 -5 -50 -50- - 50- -100 -100- -100- -150 - 150 -150 150
150
100
50
-5
- 50
-100
-150
(c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.)
Identify x-values where f"(x) > 0. (Enter your answer using interval notation.)
Identify x-values where f"(x) < 0. (Enter your answer using interval notation.)
(d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.)
Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.)
Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.)
Transcribed Image Text:150 100 50 -5 - 50 -100 -150 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your answers as a comma-separated list.) Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.)
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