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What are the critical points of f? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? f'(x) = x(x - 1) f'(x) = (x - 1)²(x + 2) f'(x) = (x − 1)(x + 2)(x − 3)

What are the critical points of f? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? f'(x) = x(x - 1) f'(x) = (x - 1)²(x + 2) f'(x) = (x − 1)(x + 2)(x − 3)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Answer the following questions about the functions whose derivatives are given below. i. ii. 111. What are the critical points of f? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? f'(x) = x(x - 1) a. b. f'(x) = (x-1)² (x + 2) c. f'(x) = (x − 1)(x + 2)(x − 3) x² (x-1) d. f'(x) x+2 O e. f'(x) = 1 - -, x = -2 4 x2 x 0 f. f'(x) = x−¹/³ (x + 2) 1/3, g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π
Transcribed Image Text:8. Answer the following questions about the functions whose derivatives are given below. i. ii. 111. What are the critical points of f? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? f'(x) = x(x - 1) a. b. f'(x) = (x-1)² (x + 2) c. f'(x) = (x − 1)(x + 2)(x − 3) x² (x-1) d. f'(x) x+2 O e. f'(x) = 1 - -, x = -2 4 x2 x 0 f. f'(x) = x−¹/³ (x + 2) 1/3, g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π
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8. Answer the following questions about the functions whose derivatives are given below. i. ii. iii. What are the critical points of f ? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? d. f'(x) = e. f'(x) = - x²(x-1) x+2 4 1 - x = 0 x2, ) x = -2 f. f'(x) = x-¹/³ (x + 2) -1/3 g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π -
Transcribed Image Text:8. Answer the following questions about the functions whose derivatives are given below. i. ii. iii. What are the critical points of f ? On what open intervals is f increasing or decreasing? At what points, if any, does f assume local maximum and minimum values? d. f'(x) = e. f'(x) = - x²(x-1) x+2 4 1 - x = 0 x2, ) x = -2 f. f'(x) = x-¹/³ (x + 2) -1/3 g. f'(x) = (sin x − 1)(2cos x + 1),0 ≤ x ≤ 2π -
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