A continuous function f, defined for all æ, has the following properties: 1. f is decreasing 2. f is concave up 3. f(9) = -2 4. f'(9) = - Sketch a possible graph for f, and use it to answer the following questions about f. A. For each of the following intervals, what is the minimum and maximum number of zeros f could have in the interval? (Note that if there must be exactly N zeros in an interval, the minimum and maximum are both N.) minimum maximum -0

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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part a-c

A continuous function f, defined for all æ, has the following properties:
1. f is decreasing
2. f is concave up
3. f(9) = -2
4. f'(9) = -
%3D
%3D
4
Sketch a possible graph for f, and use it to answer the following questions about f.
A. For each of the following intervals, what is the minimum and maximum number of zeros f could
have in the interval? (Note that if there must be exactly N zeros in an interval, the minimum and maximum
are both N.)
minimum
maximum
-o < x < 0
0 < x <1
1 < x < 9
9 < x <∞
:1.1
for f!(1)2 (Et
porotod lict
Transcribed Image Text:A continuous function f, defined for all æ, has the following properties: 1. f is decreasing 2. f is concave up 3. f(9) = -2 4. f'(9) = - %3D %3D 4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For each of the following intervals, what is the minimum and maximum number of zeros f could have in the interval? (Note that if there must be exactly N zeros in an interval, the minimum and maximum are both N.) minimum maximum -o < x < 0 0 < x <1 1 < x < 9 9 < x <∞ :1.1 for f!(1)2 (Et porotod lict
B. Are any of the following possible values for f'(1)? (Enter your answer as a comma-separated list,
or enter 'none' if none of them are possible.) –3, –2, –1, –, 0, , 1, 2, 3.
|
possible values: f'(1) =
C. What happens to f as x -o?
lim f(x) =
(Enter the value, 'infinity' or '-infinity' for oo or –o, or 'none' if there is no limit.)
Transcribed Image Text:B. Are any of the following possible values for f'(1)? (Enter your answer as a comma-separated list, or enter 'none' if none of them are possible.) –3, –2, –1, –, 0, , 1, 2, 3. | possible values: f'(1) = C. What happens to f as x -o? lim f(x) = (Enter the value, 'infinity' or '-infinity' for oo or –o, or 'none' if there is no limit.)
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