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Given the function f(x) = 2x³ + 6x 2, determine the intervals where the and decreasing, and the intervals of concavity. Write the intervals using inequalitie 2

Given the function f(x) = 2x³ + 6x 2, determine the intervals where the and decreasing, and the intervals of concavity. Write the intervals using inequalitie 2

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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Given the function f(x) = 2x³ + 6x 2, determine the intervals where the function is increasing and decreasing, and the intervals of concavity. Write the intervals using inequalities for example x < -1, 2<x<4 etc.... f(x) is increasing for: f(x) is decreasing for: f(x) is concave up for: f(x) is concave down for:
Transcribed Image Text:Given the function f(x) = 2x³ + 6x 2, determine the intervals where the function is increasing and decreasing, and the intervals of concavity. Write the intervals using inequalities for example x < -1, 2<x<4 etc.... f(x) is increasing for: f(x) is decreasing for: f(x) is concave up for: f(x) is concave down for:
Expert Solution
Step 1

f(x)=-2x3+6x-2

When function is increasing f'(x)>0

Function is increasing f'(x)<0

Function is concave up f''(x)>0

Function is concave down f''(x)<0

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