Consider the polynomial function f(x) = x - 3x3 + 3x? whose domain is (-0, 0). Find the following:

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.5: Zeros Of Polynomial Functions
Problem 80E
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How do I solve d, e, and f? 

8. Consider the polynomial function f(x) = x4 – 3x³ + 3x² whose domain is (-0, 0). Find the
following:
(a) The intervals on which f is increasing and the intervals on which it is decreasing.
(b) The open intervals on which the graph of f is concave up and the open intervals on
which the graph is concave down.
(c) The local extreme values of f.
(d) The global extreme values of f on the closed, bounded interval [-1, 2].
(e) The points of inflection of f.
(f) Sketch the graph of f on [-1, 2] using this information.
Transcribed Image Text:8. Consider the polynomial function f(x) = x4 – 3x³ + 3x² whose domain is (-0, 0). Find the following: (a) The intervals on which f is increasing and the intervals on which it is decreasing. (b) The open intervals on which the graph of f is concave up and the open intervals on which the graph is concave down. (c) The local extreme values of f. (d) The global extreme values of f on the closed, bounded interval [-1, 2]. (e) The points of inflection of f. (f) Sketch the graph of f on [-1, 2] using this information.
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