f"(x) > 0 for 2 0 if 0 4, lim f'(x) 00, lim f'(x) -o, f"(x) >0 if-14 %3D →2+ 27. f(0) =f'(0) =f'(2) =f'(4) = f'(6) = 0, f'(x) >0 if 0 6, f"(x) >0 if 0 5, f(-x) f (x) %3D concave dow 28.Suppose f(3) = 2, f'(3) =, and f'(x) > 0 and f"(x) <0 increas ng for all x. (a) Sketch a possible graph for f. (b) How many solutions does the equation f(x) 0 have? Why? (c) Is it possible that f'(2) =? Why? 29. Suppose f is a continuous function where f(x) > 0 for all x, f(0) = 4, f'(x) > 0 if x <0 or x> 2, f'(x) <0 if 0 1, f"(x)<0 if -1 0 if ated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). ng experience. Cengage Leaming reserves the right to remove additional content at any time if subsequent rights restrictions require it.
f"(x) > 0 for 2 0 if 0 4, lim f'(x) 00, lim f'(x) -o, f"(x) >0 if-14 %3D →2+ 27. f(0) =f'(0) =f'(2) =f'(4) = f'(6) = 0, f'(x) >0 if 0 6, f"(x) >0 if 0 5, f(-x) f (x) %3D concave dow 28.Suppose f(3) = 2, f'(3) =, and f'(x) > 0 and f"(x) <0 increas ng for all x. (a) Sketch a possible graph for f. (b) How many solutions does the equation f(x) 0 have? Why? (c) Is it possible that f'(2) =? Why? 29. Suppose f is a continuous function where f(x) > 0 for all x, f(0) = 4, f'(x) > 0 if x <0 or x> 2, f'(x) <0 if 0 1, f"(x)<0 if -1 0 if ated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). ng experience. Cengage Leaming reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Topic Video
Question
Number 28 part C
Transcribed Image Text:f"(x) > 0 for 2 <x< 8
26. f'(0) =f'(4) 0, f'(x) = 1 if x < -1,
f'(x) > 0 if 0 <x <2,
f'(x) <0 if-1 <x <0 or 2<x<4 or x > 4,
lim f'(x) 00, lim f'(x) -o,
f"(x) >0 if-1<x<2 or 2 <x<4,
f"(x) <0 if x >4
%3D
→2+
27. f(0) =f'(0) =f'(2) =f'(4) = f'(6) = 0,
f'(x) >0 if 0<x<2 or 4 <x<6,
f'(x) <0 if 2 <x<4 or.x> 6,
f"(x) >0 if 0 <x<1 or 3 <x< 5,
f"(x) <0 if 1 <x<3 or x > 5, f(-x) f (x)
%3D
concave
dow
28.Suppose f(3) = 2, f'(3) =, and f'(x) > 0 and f"(x) <0
increas ng
for all x.
(a) Sketch a possible graph for f.
(b) How many solutions does the equation f(x) 0 have?
Why?
(c) Is it possible that f'(2) =? Why?
29. Suppose f is a continuous function where f(x) > 0 for all x,
f(0) = 4, f'(x) > 0 if x <0 or x> 2, f'(x) <0
if 0 <x< 2, f"(-1) f"(1) = 0,
x< -1 or x> 1, f"(x)<0 if -1 <x< 1.
(a) Can f have an absolute maximum? If so, sketch a possible
graph of f. If not, explain why.
, f"(x) > 0 if
ated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
ng experience. Cengage Leaming reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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