Homework Help is Here – Start Your Trial Now!
Math
Calculus
In this question, we will consider the function f(x) = x² - 9x³ (a) Use asymptotics (as in the first week of class) to make a quick sketch of f(x). Use this sketch alone to decide which features the curve has. Select all that apply. ✓ f(x) has at least one root ✓ f(x) has at least one critical point ✓ f(x) has at least one global minimum ☐ f(x) has at least one global maximum ✓ f(x) has at least one local minimum ☐ f(x) has at least one local maximum ✓ f(x) has at least one inflection point (b) List the x-values of all roots of f(x). 0,9 (c) List the x-values of all critical points of f(x). 0, 27/4 (d) Use interval notation to indicate where f(x) is increasing. (A function is increasing if larger x-values give larger y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Increasing for x in: (27/4, Inf) (e) Use interval notation to indicate where f(x) is decreasing. (A function is decreasing if larger x-values give smaller y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Decreasing for x in: | (f) List the x-values of all local maxima of f(x). x-values of local maxima = NONE (g) List the x-values of all local minima of f(x). x-values of local minima = 27/4 (h) Use interval notation to indicate where f(x) is concave up. Concave up for x in: (-Inf,0)U(9/2, Inf) (i) Use interval notation to indicate where f(x) is concave down. Concave down for x in: (0,9/2) (j) List the x-values of all the inflection points of f. x-values of inflection points = 0, 9/2 B

In this question, we will consider the function f(x) = x² - 9x³ (a) Use asymptotics (as in the first week of class) to make a quick sketch of f(x). Use this sketch alone to decide which features the curve has. Select all that apply. ✓ f(x) has at least one root ✓ f(x) has at least one critical point ✓ f(x) has at least one global minimum ☐ f(x) has at least one global maximum ✓ f(x) has at least one local minimum ☐ f(x) has at least one local maximum ✓ f(x) has at least one inflection point (b) List the x-values of all roots of f(x). 0,9 (c) List the x-values of all critical points of f(x). 0, 27/4 (d) Use interval notation to indicate where f(x) is increasing. (A function is increasing if larger x-values give larger y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Increasing for x in: (27/4, Inf) (e) Use interval notation to indicate where f(x) is decreasing. (A function is decreasing if larger x-values give smaller y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Decreasing for x in: | (f) List the x-values of all local maxima of f(x). x-values of local maxima = NONE (g) List the x-values of all local minima of f(x). x-values of local minima = 27/4 (h) Use interval notation to indicate where f(x) is concave up. Concave up for x in: (-Inf,0)U(9/2, Inf) (i) Use interval notation to indicate where f(x) is concave down. Concave down for x in: (0,9/2) (j) List the x-values of all the inflection points of f. x-values of inflection points = 0, 9/2 B

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
See similar textbooks
icon
Related questions
Question

only part e needs an answer. 

In this question, we will consider the function f(x) = x² - 9x³ (a) Use asymptotics (as in the first week of class) to make a quick sketch of f(x). Use this sketch alone to decide which features the curve has. Select all that apply. ✓ f(x) has at least one root ✓ f(x) has at least one critical point ✓ f(x) has at least one global minimum ☐ f(x) has at least one global maximum ✓ f(x) has at least one local minimum ☐ f(x) has at least one local maximum ✓ f(x) has at least one inflection point (b) List the x-values of all roots of f(x). 0,9 (c) List the x-values of all critical points of f(x). 0, 27/4 (d) Use interval notation to indicate where f(x) is increasing. (A function is increasing if larger x-values give larger y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Increasing for x in: (27/4, Inf) (e) Use interval notation to indicate where f(x) is decreasing. (A function is decreasing if larger x-values give smaller y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Decreasing for x in: | (f) List the x-values of all local maxima of f(x). x-values of local maxima = NONE (g) List the x-values of all local minima of f(x). x-values of local minima = 27/4 (h) Use interval notation to indicate where f(x) is concave up. Concave up for x in: (-Inf,0)U(9/2, Inf) (i) Use interval notation to indicate where f(x) is concave down. Concave down for x in: (0,9/2) (j) List the x-values of all the inflection points of f. x-values of inflection points = 0, 9/2 B
Transcribed Image Text:In this question, we will consider the function f(x) = x² - 9x³ (a) Use asymptotics (as in the first week of class) to make a quick sketch of f(x). Use this sketch alone to decide which features the curve has. Select all that apply. ✓ f(x) has at least one root ✓ f(x) has at least one critical point ✓ f(x) has at least one global minimum ☐ f(x) has at least one global maximum ✓ f(x) has at least one local minimum ☐ f(x) has at least one local maximum ✓ f(x) has at least one inflection point (b) List the x-values of all roots of f(x). 0,9 (c) List the x-values of all critical points of f(x). 0, 27/4 (d) Use interval notation to indicate where f(x) is increasing. (A function is increasing if larger x-values give larger y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Increasing for x in: (27/4, Inf) (e) Use interval notation to indicate where f(x) is decreasing. (A function is decreasing if larger x-values give smaller y-values. Don't include points where the function changes from increasing to decreasing, or from decreasing to increasing.) Decreasing for x in: | (f) List the x-values of all local maxima of f(x). x-values of local maxima = NONE (g) List the x-values of all local minima of f(x). x-values of local minima = 27/4 (h) Use interval notation to indicate where f(x) is concave up. Concave up for x in: (-Inf,0)U(9/2, Inf) (i) Use interval notation to indicate where f(x) is concave down. Concave down for x in: (0,9/2) (j) List the x-values of all the inflection points of f. x-values of inflection points = 0, 9/2 B
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS