NEED ASAP!!! I'll rate positive for sure... Consider the function f(x) and its derivatives:1-x²(x² + 1)²2x(x²-3)(x²+1)3(a) [] Find the critical numbers of f(x) and show your work to justify.(b)Find the open interval(s) where f is decreasing and the open interval(s) where fisincreasing. Show your work to justify your answer.Find the x-coordinate(s) of all local minima of f, and all local maxima of f. Show your work(c)to justify.f'(x) =(e)and f"(x) =(d)Find the open intervals where f is concave up and the open intervals where fis concavedown. Show your work to justify.Find the x-coordinates of all inflection point(s) of f, and show your work to justify.

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Answered: Consider the function f(x) and its…

Math

Calculus

Consider the function f(x) and its derivatives:

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 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

100%

NEED ASAP!!! I'll rate positive for sure...

Consider the function f(x) and its derivatives:
1-x²
(x² + 1)²
2x(x²-3)
(x²+1)3
(a) [] Find the critical numbers of f(x) and show your work to justify.
(b)
Find the open interval(s) where f is decreasing and the open interval(s) where fis
increasing. Show your work to justify your answer.
Find the x-coordinate(s) of all local minima of f, and all local maxima of f. Show your work
(c)
to justify.
f'(x) =
(e)
and f"(x) =
(d)
Find the open intervals where f is concave up and the open intervals where fis concave
down. Show your work to justify.
Find the x-coordinates of all inflection point(s) of f, and show your work to justify.

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