Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x³ - x² + x (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation.) (-∞,1) U (1,∞) increasing decreasing DNE +x-8 (b) Find the relative extrema of f. relative maximum (x, y) = relative minimum (x, y) = concave downward (x, y) = (c) Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.) concave upward DNE DNE (d) Find the inflection points, if any, of f. X X X
Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x³ - x² + x (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation.) (-∞,1) U (1,∞) increasing decreasing DNE +x-8 (b) Find the relative extrema of f. relative maximum (x, y) = relative minimum (x, y) = concave downward (x, y) = (c) Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.) concave upward DNE DNE (d) Find the inflection points, if any, of f. X X X
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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Question
Transcribed Image Text:Consider the following function. (If an answer does not exist, enter DNE.)
x² + x - 8
f(x) =
(a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation.)
(-∞0,1) U (1,000)
increasing
decreasing
1
DNE
(b) Find the relative extrema of f.
relative maximum (x, y)
relative minimum (x, y)
concave upward
concave downward
(x, y):
=
=
=
(c) Find the intervals where the graph of f is concave upward and where it is concave downward. (Enter your answers using interval notation.)
DNE
DNE
(d) Find the inflection points, if any, of f.
)
X
›)
X
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