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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
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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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 ) )
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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