f'(x) < 0 for -3 < x < 0 f'(x) < 0 for 3 < x < 4 f'(x) > 0 for -4 < x < -3 f'(x) > 0 for 0 0 for − 3 < x < ² 2 3 f"(x) < 0 for -4 < x < -² 2 3 f" (x) < 0 for = < x < 4 3 f"(x) = 0 at x = -and x = 1/ 2 f(0) = -3

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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Question

A continuous function has the following properties. Use the information to sketch a possible graph of the function f.

f'(x) < 0 for -3 < x < 0
f'(x) < 0 for 3 < x < 4
f'(x) > 0 for -4 < x < -3
f'(x) > 0 for 0 < x < 3
f'(x) = 0 at x = -3, x = 0, x = 3
3
f'(x) > 0 for -< x <
2
3
ƒ"(x) < 0 for −4 < x < - 1²/2
3
ƒ"(x) < 0 for ³ < x < 4
NIW
3
3
ƒ"(x) = 0 at x = -²- and x = 1/2
=
2
f(0) = -3
Transcribed Image Text:f'(x) < 0 for -3 < x < 0 f'(x) < 0 for 3 < x < 4 f'(x) > 0 for -4 < x < -3 f'(x) > 0 for 0 < x < 3 f'(x) = 0 at x = -3, x = 0, x = 3 3 f'(x) > 0 for -< x < 2 3 ƒ"(x) < 0 for −4 < x < - 1²/2 3 ƒ"(x) < 0 for ³ < x < 4 NIW 3 3 ƒ"(x) = 0 at x = -²- and x = 1/2 = 2 f(0) = -3
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