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Given the function f(x) = x³ 6x² + 9x - 4 a) Find the first derivative and the critical numbers and use them to make a sign diagram for the first derivative showing the intervals of increase and decrease for the function. b) Find the second derivative and the possible inflection points and use them to make a sign diagram for the second derivative showing the intervals of concavity for the function. c) Use the information to make a table of values and sketch a comprehensive graph of the function. Show the local mins and maximums and the inflection points on the graph.

Given the function f(x) = x³ 6x² + 9x - 4 a) Find the first derivative and the critical numbers and use them to make a sign diagram for the first derivative showing the intervals of increase and decrease for the function. b) Find the second derivative and the possible inflection points and use them to make a sign diagram for the second derivative showing the intervals of concavity for the function. c) Use the information to make a table of values and sketch a comprehensive graph of the function. Show the local mins and maximums and the inflection points on the graph.

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) = x³− 6x² + 9x - 4 a) Find the first derivative and the critical numbers and use them to make a sign diagram for the first derivative showing the intervals of increase and decrease for the function. b) Find the second derivative and the possible inflection points and use them to make a sign diagram for the second derivative showing the intervals of concavity for the function. c) Use the information to make a table of values and sketch a comprehensive graph of the function. Show the local mins and maximums and the inflection points on the graph.
Transcribed Image Text:Given the function f(x) = x³− 6x² + 9x - 4 a) Find the first derivative and the critical numbers and use them to make a sign diagram for the first derivative showing the intervals of increase and decrease for the function. b) Find the second derivative and the possible inflection points and use them to make a sign diagram for the second derivative showing the intervals of concavity for the function. c) Use the information to make a table of values and sketch a comprehensive graph of the function. Show the local mins and maximums and the inflection points on the graph.
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