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Follow the 5 Steps for Curve Sketching to sketch the graph of the function. f (x) = ²-x²-3 Step 1: Find the critical points and plot them on the graph on the next page. a. Find the first derivative. b. Set the first derivative equal to 0 and find where the first derivative does not exist. c. Plug the x-value of each critical point into the original function to find the y-value of the point itself. 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 f'(x) Behavior of f(x)

Follow the 5 Steps for Curve Sketching to sketch the graph of the function. f (x) = ²-x²-3 Step 1: Find the critical points and plot them on the graph on the next page. a. Find the first derivative. b. Set the first derivative equal to 0 and find where the first derivative does not exist. c. Plug the x-value of each critical point into the original function to find the y-value of the point itself. 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 f'(x) Behavior of f(x)

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. r3 f (x) = - x²-3x 3 Step 1: Find the critical points and plot them on the graph on the next page. Find the first derivative. a. b. Set the first derivative equal to 0 and find where the first derivative does not exist. c. Plug the x-value of each critical point into the original function to find the y-value of the point itself. 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 f'(x) Behavior of f(x) (Steps continued on the next page) Step 3: Find the possible inflection points and plot them on the graph below. a. Find the second derivative. b. Set the second derivative equal to 0 and find where the second derivative does not exist. c. Plug the x-value of each possible point of inflection into the original function to find the y-value of the point itself. 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 Sign of f(x) Behavior of f(x) Step 5: Sketch the curve. tv
Transcribed Image Text:Follow the 5 Steps for Curve Sketching to sketch the graph of the function. r3 f (x) = - x²-3x 3 Step 1: Find the critical points and plot them on the graph on the next page. Find the first derivative. a. b. Set the first derivative equal to 0 and find where the first derivative does not exist. c. Plug the x-value of each critical point into the original function to find the y-value of the point itself. 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 f'(x) Behavior of f(x) (Steps continued on the next page) Step 3: Find the possible inflection points and plot them on the graph below. a. Find the second derivative. b. Set the second derivative equal to 0 and find where the second derivative does not exist. c. Plug the x-value of each possible point of inflection into the original function to find the y-value of the point itself. 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 Sign of f(x) Behavior of f(x) Step 5: Sketch the curve. tv
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