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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
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 28E
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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
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