Homework Help is Here – Start Your Trial Now!
Math
Calculus
y = x - 15 x 10 y = x (4, 4) -6 -4 4 K-4,-4) - 10 - 20 20

y = x - 15 x 10 y = x (4, 4) -6 -4 4 K-4,-4) - 10 - 20 20

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...
See similar textbooks
icon
Related questions
Question
Find the area of the shaded region
The image shows a graph with two curves plotted on a Cartesian plane. The curves represent the functions \( y = x^3 - 15x \) and \( y = x \). ### Graph Description: 1. **Function \( y = x^3 - 15x \):** - This is a cubic function displayed in blue. - It exhibits typical cubic behavior, with an S-like shape crossing the x-axis multiple times. - The curve is shaded in blue below it to highlight the area under the curve. 2. **Function \( y = x \):** - This is a linear function represented by a red line. - It passes through the origin and rises diagonally, intersecting the cubic curve. 3. **Intersection Points:** - The red line intersects the blue curve at two points: - \((-4, -4)\): This point is on the left side where the cubic function crosses the line. - \((4, 4)\): This point is on the right side, another intersection of the functions. 4. **Axes:** - The x-axis ranges from \(-6\) to \(6\). - The y-axis ranges from \(-20\) to \(20\). ### Observations: - The cubic function has two turning points, creating a local maximum and minimum. - The intersection points provide solutions to the equation \( x^3 - 15x = x \). This visualization is helpful for understanding the behavior and intersections of cubic and linear functions on a graph.
Transcribed Image Text:The image shows a graph with two curves plotted on a Cartesian plane. The curves represent the functions \( y = x^3 - 15x \) and \( y = x \). ### Graph Description: 1. **Function \( y = x^3 - 15x \):** - This is a cubic function displayed in blue. - It exhibits typical cubic behavior, with an S-like shape crossing the x-axis multiple times. - The curve is shaded in blue below it to highlight the area under the curve. 2. **Function \( y = x \):** - This is a linear function represented by a red line. - It passes through the origin and rises diagonally, intersecting the cubic curve. 3. **Intersection Points:** - The red line intersects the blue curve at two points: - \((-4, -4)\): This point is on the left side where the cubic function crosses the line. - \((4, 4)\): This point is on the right side, another intersection of the functions. 4. **Axes:** - The x-axis ranges from \(-6\) to \(6\). - The y-axis ranges from \(-20\) to \(20\). ### Observations: - The cubic function has two turning points, creating a local maximum and minimum. - The intersection points provide solutions to the equation \( x^3 - 15x = x \). This visualization is helpful for understanding the behavior and intersections of cubic and linear functions on a graph.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS