Consider a continuous function f(x). The function has critical points at x = 0, x = 2, and x = 3. The table below shows the open intervals between each of these critical points and the sign of f'(x) on each interval. At what value(s) of x do any local maxima occur? Select all that apply. Select the correct answer below: Ox=0 O x = 2 Interval (-∞, 0) (0, 2) (2,3) (3,00) Ox=3 Sign of f'(x) at Test Point O The function does not have a local maximum. Conclusion f(x) is decreasing f(x) is decreasing f(x) is increasing f(x) is decreasing

College Algebra (MindTap Course List)
12th Edition
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Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Consider a continuous function f(x). The function has critical points at x = 0, x = 2, and x = 3. The table below shows the
open intervals between each of these critical points and the sign of f'(x) on each interval. At what value(s) of x do any local
maxima occur? Select all that apply.
O x = 0
Select the correct answer below:
O x = 2
Interval
(-∞0, 0)
(0, 2)
O x = 3
(2,3)
(3,00)
Sign of f'(x) at Test Point
The function does not have a local maximum.
+
Conclusion
f(x) is decreasing
f(x) is decreasing
f(x) is increasing
f(x) is decreasing
Transcribed Image Text:Consider a continuous function f(x). The function has critical points at x = 0, x = 2, and x = 3. The table below shows the open intervals between each of these critical points and the sign of f'(x) on each interval. At what value(s) of x do any local maxima occur? Select all that apply. O x = 0 Select the correct answer below: O x = 2 Interval (-∞0, 0) (0, 2) O x = 3 (2,3) (3,00) Sign of f'(x) at Test Point The function does not have a local maximum. + Conclusion f(x) is decreasing f(x) is decreasing f(x) is increasing f(x) is decreasing
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