[2] Let f(x) be a polynomial function. Its derivative is given by f'(x) = (x – 2)³(x + 1). Identify the following: %3D a) The critical numbers and critical points of the function f(x). b) The intervals where the function f(x) is increasing and decreasing. c) The relative maximum and relative minimum of the graph of f(x). Note: Use appropriate notations for values that cannot be exactly determined.

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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[2] Let f(x) be a polynomial function. Its derivative is given by f'(x) = (x – 2)³ (x + 1). Identify the
following:
a) The critical numbers and critical points of the function f(x).
b) The intervals where the function f(x) is increasing and decreasing.
c) The relative maximum and relative minimum of the graph of f(x).
Note: Use appropriate notations for values that cannot be exactly determined.
Transcribed Image Text:[2] Let f(x) be a polynomial function. Its derivative is given by f'(x) = (x – 2)³ (x + 1). Identify the following: a) The critical numbers and critical points of the function f(x). b) The intervals where the function f(x) is increasing and decreasing. c) The relative maximum and relative minimum of the graph of f(x). Note: Use appropriate notations for values that cannot be exactly determined.
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