For the function graphed below, find the values of x at which the derivative does not exist. (Enter your answers as a comma-separated list.) X = د 2 4 x
For the function graphed below, find the values of x at which the derivative does not exist. (Enter your answers as a comma-separated list.) X = د 2 4 x
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...
Related questions
Question
![### Identifying Points Where Derivatives Do Not Exist
**Problem Statement:**
_Examine the given function graph and determine the values of \(x\) at which the derivative does not exist. Provide your answers as a comma-separated list._
**Graph Description:**
- The graph is plotted on the \(xy\)-coordinate system.
- The x-axis ranges from \(-4\) to \(4\), and the y-axis values shown range from \(-2\) to unspecified.
**Key Observations in the Graph:**
1. **Discontinuity at \((x = -3)\)**: There is a break in the graph where the function value suddenly jumps from one point to another, indicating a discontinuity. The point at \(x = -3\) appears to be undefined due to the discontinuity.
- There is an open circle at approximately \((-3, 1.5)\), showing where the function value is missing.
- There is a solid dot slightly below the open circle, indicating an immediate function value just before or after \(x = -3\).
2. **Sharp Corner or Cusp at \((x = 2)\)**: The graph displays a noticeable "kink" or abrupt change in direction at \(x = 2\).
- Before \(x = 2\), the graph is descending.
- Immediately after \(x = 2\), the graph changes to an ascending direction.
**Conclusion:**
The values of \(x\) where the derivative does not exist are due to the discontinuity and the sharp corner in the graph.
**Answer:**
\[ x = -3, 2 \]
**Note:** Analyze such points carefully in any function to determine the points of non-existent derivatives, taking into account both discontinuities and sharp bends or cusps.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e0cd55c-6f84-412a-ac81-9a79eaea810f%2F0ac2aad6-9af6-4ef6-a609-d962c7c87d41%2F5e8e536_processed.png&w=3840&q=75)
Transcribed Image Text:### Identifying Points Where Derivatives Do Not Exist
**Problem Statement:**
_Examine the given function graph and determine the values of \(x\) at which the derivative does not exist. Provide your answers as a comma-separated list._
**Graph Description:**
- The graph is plotted on the \(xy\)-coordinate system.
- The x-axis ranges from \(-4\) to \(4\), and the y-axis values shown range from \(-2\) to unspecified.
**Key Observations in the Graph:**
1. **Discontinuity at \((x = -3)\)**: There is a break in the graph where the function value suddenly jumps from one point to another, indicating a discontinuity. The point at \(x = -3\) appears to be undefined due to the discontinuity.
- There is an open circle at approximately \((-3, 1.5)\), showing where the function value is missing.
- There is a solid dot slightly below the open circle, indicating an immediate function value just before or after \(x = -3\).
2. **Sharp Corner or Cusp at \((x = 2)\)**: The graph displays a noticeable "kink" or abrupt change in direction at \(x = 2\).
- Before \(x = 2\), the graph is descending.
- Immediately after \(x = 2\), the graph changes to an ascending direction.
**Conclusion:**
The values of \(x\) where the derivative does not exist are due to the discontinuity and the sharp corner in the graph.
**Answer:**
\[ x = -3, 2 \]
**Note:** Analyze such points carefully in any function to determine the points of non-existent derivatives, taking into account both discontinuities and sharp bends or cusps.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning