Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![III. Suppose that a function f(x) satisfies the following properties, together with the table of signs
given below.
dom f = R\ {-1}
●
lim [f(x)(1-x)] = 0
x--00
lim f(x) = 2
●
lim_f(x) = = -00
x→−1¯
●
lim f(x) = +00
x-1+
(-∞, -1)
-1
(-1,0)
(0,2)
2
(2, +00)
f
und
0
f'
und
0
+
+
+
f"
und
+
+
+
0
1. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equations
and label all relative extremum point/s and point/s of inflection with their coordinates.
00++x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e41d0c3-bb4b-4ce6-ac75-c15fb33c1dd2%2F326cf9c7-de84-4a82-853f-81ca7aef8d7b%2Fblx36c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:III. Suppose that a function f(x) satisfies the following properties, together with the table of signs
given below.
dom f = R\ {-1}
●
lim [f(x)(1-x)] = 0
x--00
lim f(x) = 2
●
lim_f(x) = = -00
x→−1¯
●
lim f(x) = +00
x-1+
(-∞, -1)
-1
(-1,0)
(0,2)
2
(2, +00)
f
und
0
f'
und
0
+
+
+
f"
und
+
+
+
0
1. Sketch a possible graph of f with emphasis on concavity. Label asymptotes with their equations
and label all relative extremum point/s and point/s of inflection with their coordinates.
00++x
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