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Follow the 5 Steps for Curve Sketching to sketch the graph of the function 9(x) = 2x³-2 x1/3 Step 1: Find the critical points and plot them on the graph below. Step 2: Use the table below to test the regions to see where the function increases or decreases. Include your work for determining the sign of each interval. Intervals Sign of g'(x) Behavior of g(x) Step 3: Find the possible inflection points and plot them on the graph below.

Follow the 5 Steps for Curve Sketching to sketch the graph of the function 9(x) = 2x³-2 x1/3 Step 1: Find the critical points and plot them on the graph below. Step 2: Use the table below to test the regions to see where the function increases or decreases. Include your work for determining the sign of each interval. Intervals Sign of g'(x) Behavior of g(x) Step 3: Find the possible inflection points and plot them on the graph below.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Follow the 5 Steps for Curve Sketching to sketch the graph of the function 2x³ - 2 x1/3 Step 1: Find the critical points and plot them on the graph below. Intervals Step 2: Use the table below to test the regions to see where the function increases or decreases. Include your work for determining the sign of each interval. Sign of g'(x) Behavior of g(x) ●●● Step 3: Find the possible inflection points and plot them on the graph below. Sign of g"(x) Behavior of g(x) Step 4: Use the table below to test for the concavity of the function. Include your work for determining the sign of each interval. Intervals g(x) = Step 5: Sketch the curve. Intervals Sign of h'(x) Sign of h"(x) Part 3: Oh no! While you were working on your calculus homework at your favorite coffee shop, you accidentally spill your coffee on your paper. The coffee spilled all over the equations for the function and its derivatives, but thankfully the rest of your work was saved. ← Using the information below, sketch the graph of h(x). (10 points) h(x) = h'(x) = h"(x) = x <-4 Positive Negative ty h'(x): Critical points at x = -4, x = 1, x = 3 h"(x): Possible inflection points at x = -4,x= -1, x= 3 Points: h(-4)= 0; h(-1) = 3; h(1) = 8; h(3) is undefined; h(5) = 2 ty x > 3 -4<x<-1 -1<x<1 1<x<3 Positive Positive Negative Negative Positive Negative Negative Positive >
Transcribed Image Text:Follow the 5 Steps for Curve Sketching to sketch the graph of the function 2x³ - 2 x1/3 Step 1: Find the critical points and plot them on the graph below. Intervals Step 2: Use the table below to test the regions to see where the function increases or decreases. Include your work for determining the sign of each interval. Sign of g'(x) Behavior of g(x) ●●● Step 3: Find the possible inflection points and plot them on the graph below. Sign of g"(x) Behavior of g(x) Step 4: Use the table below to test for the concavity of the function. Include your work for determining the sign of each interval. Intervals g(x) = Step 5: Sketch the curve. Intervals Sign of h'(x) Sign of h"(x) Part 3: Oh no! While you were working on your calculus homework at your favorite coffee shop, you accidentally spill your coffee on your paper. The coffee spilled all over the equations for the function and its derivatives, but thankfully the rest of your work was saved. ← Using the information below, sketch the graph of h(x). (10 points) h(x) = h'(x) = h"(x) = x <-4 Positive Negative ty h'(x): Critical points at x = -4, x = 1, x = 3 h"(x): Possible inflection points at x = -4,x= -1, x= 3 Points: h(-4)= 0; h(-1) = 3; h(1) = 8; h(3) is undefined; h(5) = 2 ty x > 3 -4<x<-1 -1<x<1 1<x<3 Positive Positive Negative Negative Positive Negative Negative Positive >
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