Give an example of a function f(x) such that f' (0)=0 but f"(0) does not exist, and state whether f has a minimum or maximum, or an inflection point at x D0. Choose the correct answer below. O A. fX) =x°, with a relative minimum at x = 0 B. fx)=x with a relative minimum at x-0 1X) =x, with an inflection point at x = 0 f(X) =x*, with a relative maximum at x = 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...
Question
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Give an example of a function f(x) such that f' (0) = 0 but f"(0) does not exist, and state whether f has
a minimum or maximum, or an inflection point at x D0.
Choose the correct answer below.
O A.
fX) =x°, with a relative minimum at x = 0
3.
B.
f(X) =x
with a relative minimum atx=0
C.
f(X) =x, with an inflection point at x = 0
D.
f(X) =x*, with a relative maximum at x = 0
Transcribed Image Text:Give an example of a function f(x) such that f' (0) = 0 but f"(0) does not exist, and state whether f has a minimum or maximum, or an inflection point at x D0. Choose the correct answer below. O A. fX) =x°, with a relative minimum at x = 0 3. B. f(X) =x with a relative minimum atx=0 C. f(X) =x, with an inflection point at x = 0 D. f(X) =x*, with a relative maximum at x = 0
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