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33. Let f be a function with derivative given by ƒ'(x) = x³ − 5x² + e*. On which of the following intervals is the graph of f concave down? (A) (-∞, 0.117) only (B) (-∞, 1.144) (C) (0.116,2.062) (D) (0.673, 2.863) (E) (2.863, ∞)

33. Let f be a function with derivative given by ƒ'(x) = x³ − 5x² + e*. On which of the following intervals is the graph of f concave down? (A) (-∞, 0.117) only (B) (-∞, 1.144) (C) (0.116,2.062) (D) (0.673, 2.863) (E) (2.863, ∞)

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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33. Let f be a function with derivative given by f'(x) = x' – 5x? + e*. On which of the following intervals is the graph of f concave down? (A) (-00, 0.117) only (B) (-00, 1.144) (C) (0.116, 2.062) (D) (0.673, 2.863) (E) (2.863, o0) 34. What is the average value of y = Jcos x on the interval 0 < x <? (A) -0.637 (B) 0.500 (C) 0.763 (D) 1.198 (E) 1.882 35. Let y = f(x) be the solution to the differential equation = x - y with initial condition f(1) = 3. What is dx the approximation for f(2) obtained by using Euler's method with two steps of equal length starting at x = 1? 7 (A) 4 (C) 4 21 (E) 4 (В) 1 (D) 2
Transcribed Image Text:33. Let f be a function with derivative given by f'(x) = x' – 5x? + e*. On which of the following intervals is the graph of f concave down? (A) (-00, 0.117) only (B) (-00, 1.144) (C) (0.116, 2.062) (D) (0.673, 2.863) (E) (2.863, o0) 34. What is the average value of y = Jcos x on the interval 0 < x <? (A) -0.637 (B) 0.500 (C) 0.763 (D) 1.198 (E) 1.882 35. Let y = f(x) be the solution to the differential equation = x - y with initial condition f(1) = 3. What is dx the approximation for f(2) obtained by using Euler's method with two steps of equal length starting at x = 1? 7 (A) 4 (C) 4 21 (E) 4 (В) 1 (D) 2
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