Consider the function f(x)= x³ + x²-x+1. a. Determine the concavity of the graph off by making a sign chart of the second derivative function. b. Find all the inflection points of f. c. Determine where f is increasing and decreasing by making a sign chart of the first derivative function. d. Combine your answers to a. and b. to investigate the nature of the increasing and decreasing behavior of f. e. Verify your answers by making the graph off with your graphical calculator.
Consider the function f(x)= x³ + x²-x+1. a. Determine the concavity of the graph off by making a sign chart of the second derivative function. b. Find all the inflection points of f. c. Determine where f is increasing and decreasing by making a sign chart of the first derivative function. d. Combine your answers to a. and b. to investigate the nature of the increasing and decreasing behavior of f. e. Verify your answers by making the graph off with your graphical calculator.
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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Transcribed Image Text:5. Consider the function f(x) = x³ + x² − x +1.
a. Determine the concavity of the graph of f by making a sign chart of the second derivative function.
b. Find all the inflection points of f.
c. Determine where f is increasing and decreasing by making a sign chart of the first derivative
function.
d. Combine your answers to a. and b. to investigate the nature of the increasing and decreasing
behavior of f.
e. Verify your answers by making the graph of f with your graphical calculator.
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