(u) T'Imu Che X-Value(s) of the point of inf 2. Sketch the graph of a function f that satis (a) f(-1) =4, f(1) = -2, and f(3) = %3D (b) f'(-1) = f'(1) = f'(3) = 0, %D (c) f'(x) > 0 if x <-1 or 1 3, (e) f"(x) > 0 if 0 < x < 2, (f) f"(x) <0 if x <0 or x > 2.

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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Number 2

f(x)% 336x+3x-2r3
(a) Find the interval(s) where f is increasing or decreasing.
(b) Find the local maximum and minimum values.
(c) Find the interval(s) where f is concave up or concave down.
(d) Find the x-value(s) of the point of inflection.
2. Sketch the graph of a function f that satisfies all of the given conditions.
(a) f(-1) = 4, f(1) = -2, and f(3) = 1,
(b) f'(-1) = f'(1) = f'(3) = 0,
%3D
%3D
(c) f'(x) > 0 if x <-1 or 1 <x < 3,
(d)
f'(x) <0 if -1 <x <1 or x > 3,
(e) f"(x) >0 if 0 < x < 2,
(f) f"(x) < 0 if x <0 or x > 2.
3. Find the following limits using l'Hospital's Rule.
1- sin 0
(а) lim
0→1+cos 20
x + x2
(b) lim
x00 1-2x2
(c) lim 5x?e-20
Transcribed Image Text:f(x)% 336x+3x-2r3 (a) Find the interval(s) where f is increasing or decreasing. (b) Find the local maximum and minimum values. (c) Find the interval(s) where f is concave up or concave down. (d) Find the x-value(s) of the point of inflection. 2. Sketch the graph of a function f that satisfies all of the given conditions. (a) f(-1) = 4, f(1) = -2, and f(3) = 1, (b) f'(-1) = f'(1) = f'(3) = 0, %3D %3D (c) f'(x) > 0 if x <-1 or 1 <x < 3, (d) f'(x) <0 if -1 <x <1 or x > 3, (e) f"(x) >0 if 0 < x < 2, (f) f"(x) < 0 if x <0 or x > 2. 3. Find the following limits using l'Hospital's Rule. 1- sin 0 (а) lim 0→1+cos 20 x + x2 (b) lim x00 1-2x2 (c) lim 5x?e-20
Expert Solution
Step 1

Given:

a)f(-1)=4, f(1)=2, f(3)=1

b) f'(-1)=f'(1)=f'(3)=0

c) f'(x)>0 if x<-1 or 1<x<3.

d) f'(x)<0 if -1<x<1 or x>3 

e) f"(x)>0 if 0<x<2 

f) f"(x)<0 if x<0 or x>2.

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