Consider the function f(x) = 2x4 - 8x3. (a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (If an answer does not exist, enter DNE.) (x, y) = | (smaller x-value) (x, y) = (larger x-value) (b) Find an equation for each horizontal tangent line. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.) (c) Solve the inequality f'(x) > 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) (d) Solve the inequality f'(x) < 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) (e) Graph fand any horizontal lines found in (b) on the same set of axes. (A graphing calculator is recommended.) 40 4아 20 20 -10 10 -10 -5 10 -20 20 -40아 -40 ---- (b)
Consider the function f(x) = 2x4 - 8x3. (a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (If an answer does not exist, enter DNE.) (x, y) = | (smaller x-value) (x, y) = (larger x-value) (b) Find an equation for each horizontal tangent line. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.) (c) Solve the inequality f'(x) > 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) (d) Solve the inequality f'(x) < 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) (e) Graph fand any horizontal lines found in (b) on the same set of axes. (A graphing calculator is recommended.) 40 4아 20 20 -10 10 -10 -5 10 -20 20 -40아 -40 ---- (b)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
![y
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f
1---
(f) Describe the graph of f for the results obtained in parts (c) and (d).
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Transcribed Image Text:y
40
40
-10
-5
5
10
-10
-5
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-40-
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f
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(f) Describe the graph of f for the results obtained in parts (c) and (d).
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![Consider the function f(x) = 2x4 - 8x3.
(a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (If an answer does not exist, enter DNE.)
(х, у)
(smaller x-value)
(х, у) 3
(larger x-value)
(b) Find an equation for each horizontal tangent line. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.)
(c) Solve the inequality f'(x) > 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
(d) Solve the inequality f'(x) < 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
(e) Graph f and any horizontal lines found in (b) on the same set of axes. (A graphing calculator is recommended.)
y
y
40
40
-10
-5
10
-10
-5
5
10
-20
20
-40 -
-40
f
f
(b)
5-11
20
20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F831b8910-ac59-4660-b346-77daf4df7bac%2F880ee1c0-97ab-4c71-a9c0-9c898eddb9b4%2Fixnndse_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function f(x) = 2x4 - 8x3.
(a) Find the points, if any, at which the graph of each function f has a horizontal tangent line. (If an answer does not exist, enter DNE.)
(х, у)
(smaller x-value)
(х, у) 3
(larger x-value)
(b) Find an equation for each horizontal tangent line. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list of equations.)
(c) Solve the inequality f'(x) > 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
(d) Solve the inequality f'(x) < 0. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)
(e) Graph f and any horizontal lines found in (b) on the same set of axes. (A graphing calculator is recommended.)
y
y
40
40
-10
-5
10
-10
-5
5
10
-20
20
-40 -
-40
f
f
(b)
5-11
20
20
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