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8. Given the function f(x) = -x³ + x² a) Determine the intervals in which the function is increasing and decreasing and find the coordinates of the relative maximum or minimum.

8. Given the function f(x) = -x³ + x² a) Determine the intervals in which the function is increasing and decreasing and find the coordinates of the relative maximum or minimum.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Given the function f(x) = x³ + x² a) Determine the intervals in which the function is increasing and decreasing and find the coordinates of the relative maximum or minimum. b) Find the intervals of concavity and the coordinates of any points of inflection. c) Sketch the graph of the function and label its extreme values and its points of inflection.
Transcribed Image Text:8. Given the function f(x) = x³ + x² a) Determine the intervals in which the function is increasing and decreasing and find the coordinates of the relative maximum or minimum. b) Find the intervals of concavity and the coordinates of any points of inflection. c) Sketch the graph of the function and label its extreme values and its points of inflection.
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