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Consider the following. f(x) = x³-6x² + 3 (a) Find f'(x) and f"(x). 3x² - 12x f'(x) = f"(x) = 6x - 12 y Good job. (b) Graph f(x), f'(x), and f"(x) with a graphing utility. 150 Perfect!

Consider the following. f(x) = x³-6x² + 3 (a) Find f'(x) and f"(x). 3x² - 12x f'(x) = f"(x) = 6x - 12 y Good job. (b) Graph f(x), f'(x), and f"(x) with a graphing utility. 150 Perfect!

Calculus: Early Transcendentals
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 + 3 (a) Find f'(x) and f"(x). f'(x) = 3x² - 12x f"(x) 6x - 12 -5 (b) Graph f(x), f'(x), and f"(x) with a graphing utility. 150 100 50 -50 - 100 y - 150 Good job. Perfect! O -5 100 59 -50 150 -100 y
Transcribed Image Text:Consider the following. f(x) = x³ - 6x² + 3 (a) Find f'(x) and f"(x). f'(x) = 3x² - 12x f"(x) 6x - 12 -5 (b) Graph f(x), f'(x), and f"(x) with a graphing utility. 150 100 50 -50 - 100 y - 150 Good job. Perfect! O -5 100 59 -50 150 -100 y
x = 2 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) Nicely done! Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) (2,00) -150 Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (-∞0,2) Fantastic job! (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your ans x = (6,- 12) X Good job! Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) (-∞,2) U(-12,∞) X Way to go! Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.) (2, -12) Need Help? X Interval notation has the smaller number on the left and the larger number on the right. Read it X (e) When f(x) has a maximum point, is f"(x) > 0 or f"(x) < 0? Of"(x) > 0 f"(x) < 0 Excellent job! (f) When f(x) has a minimum point, is f"(x) > 0 or f"(x) < 0? F"(x) > 0 O F"(x) < 0 15
Transcribed Image Text:x = 2 (c) Identify x-values where f"(x) = 0. (Enter your answers as a comma-separated list.) Nicely done! Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) (2,00) -150 Identify x-values where f"(x) < 0. (Enter your answer using interval notation.) (-∞0,2) Fantastic job! (d) Identify x-values where f'(x) has a maximum point or a minimum point. (Enter your ans x = (6,- 12) X Good job! Identify x-values where f'(x) is increasing. (Enter your answer using interval notation.) (-∞,2) U(-12,∞) X Way to go! Identify x-values where f'(x) is decreasing. (Enter your answer using interval notation.) (2, -12) Need Help? X Interval notation has the smaller number on the left and the larger number on the right. Read it X (e) When f(x) has a maximum point, is f"(x) > 0 or f"(x) < 0? Of"(x) > 0 f"(x) < 0 Excellent job! (f) When f(x) has a minimum point, is f"(x) > 0 or f"(x) < 0? F"(x) > 0 O F"(x) < 0 15
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