Consider f(x) = x3+6x2-15x+2 a) Find the critical numbers and the open intervals on which the function is increasing or decreasing; b) Find any relative minimum and relative maximum; c) Find the open intervals on which the function is concave upward or concave downward, identify all the points of inflection, if any. d) If the function f is restricted to the interval [-6,5], find the absolute minimum and absolute maximum. e) Determine whether the Mean Value Theorem can be applied to f on [0,2]. If the Mean Value Theorem can be applied, find all value(s) of c in the open interval (0,2) that satisfies the theorem.

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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Consider f(x) = x3+6x2-15x+2

a) Find the critical numbers and the open intervals on which the function is increasing or decreasing;

b) Find any relative minimum and relative maximum;

c) Find the open intervals on which the function is concave upward or concave downward, identify all the points of inflection, if any.

d) If the function f is restricted to the interval [-6,5], find the absolute minimum and absolute maximum.

e) Determine whether the Mean Value Theorem can be applied to f on [0,2]. If the Mean Value Theorem can be applied, find all value(s) of c in the open interval (0,2) that satisfies the theorem.

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