Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x4 - 32x² (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation.) (-4,0) U (4,∞0) increasing decreasing (b) Find the relative extrema of f. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = relative maximum relative minima -∞, -4) U (0,4) concave downward (x, y) = (x, y) = (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 X X X X X X (d) Find the inflection points, if any, of f. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = ) X
Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x4 - 32x² (a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation.) (-4,0) U (4,∞0) increasing decreasing (b) Find the relative extrema of f. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = relative maximum relative minima -∞, -4) U (0,4) concave downward (x, y) = (x, y) = (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 X X X X X X (d) Find the inflection points, if any, of f. (Order your answers from smallest to largest x, then from smallest to largest y.) (x, y) = ) 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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Transcribed Image Text:Consider the following function. (If an answer does not exist, enter DNE.)
f(x) = x4 - 32x²2
(a) Find the intervals where the function f is increasing and where it is decreasing. (Enter your answers using interval notation.)
(-4,0) U (4,00)
(-∞, -4) U (0,4)
increasing
decreasing
(b) Find the relative extrema of f. (Order your answers from smallest to largest x, then from smallest to largest y.)
(x, y) =
relative maximum
relative minima
concave downward
(x, y)
(x, y)
=
(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
X
(d) Find the inflection points, if any, of f. (Order your answers from smallest to largest x, then from smallest to largest y.)
(x, y)
X
)
)
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