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
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Please do all three part of these questions. Thank you for your help. 

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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