Sketch the graph of the function based on the information givena. fl-4) = f(-1) = f(3) = 0, f(0) = 4%3Db. limx→-2 f(x) = -00%3Dc.f' (0) = f' (3) = 0d. f" (-4) = f " (2) = 0e. fx '() >0 if-2 3f.fx '()<0 if x <-2 or 0< x < 3g. f" (x) > 0 if x <-4 or x > 2h. fx "() <0 if -4 < x < -2 or -2

b let fx=1x+2limx→-2fx=limx→-21x+2limx→-2fx=-∞so function is fx=1x+2

Answered: b. limx>-2 f(x) = -00 c.f' (0) = f' (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

Sketch the graph of the function based on the information given
a. fl-4) = f(-1) = f(3) = 0, f(0) = 4
%3D
b. limx→-2 f(x) = -00
%3D
c.f' (0) = f' (3) = 0
d. f" (-4) = f " (2) = 0
e. fx '() >0 if-2 <x < 0 or x> 3
f.fx '()<0 if x <-2 or 0< x < 3
g. f" (x) > 0 if x <-4 or x > 2
h. fx "() <0 if -4 < x < -2 or -2 <x < 2

Expert Solution

Step 1

$(b) l e t f (x) = \frac{1}{x + 2} \lim_{x \to - 2} f (x) = \lim_{x \to - 2} \frac{1}{x + 2} \lim_{x \to - 2} f (x) = - \infty s o f u n c t i o n i s f (x) = \frac{1}{x + 2}$

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