Consider the graph of y=g(x). Graph attached below. List the following in ascending order(lowest to highest). a) g'(−3) b) g'(−2) c) g'(−1) d) g'(2)
Consider the graph of y=g(x). Graph attached below. List the following in ascending order(lowest to highest). a) g'(−3) b) g'(−2) c) g'(−1) d) g'(2)
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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Consider the graph of y=g(x).
Graph attached below.
List the following in ascending order(lowest to highest).
a) g'(−3) b) g'(−2) c) g'(−1) d) g'(2)
![---
**Consider the graph of \( y = g(x) \).**
![Graph]
The graph depicts the function \( g(x) \) and includes the following points of interest:
- X-axis ranges from \(-4\) to \(4\).
- Y-axis ranges from \(-2\) to \(2\).
### Key Plot Points:
- The curve starts at approximately \(( -4, 0.5 )\), reaches a peak just above \(1\) at around \(x = -3\), and then descends crossing the x-axis between \(-2\) and \(-1\).
- The curve reaches its lowest point just below \(-1\) at about \(x = -1\), then ascends, crossing the x-axis again around \(x = 1\).
- The graph appears to linearly increase from \(x = 2\) onward past \(y = 1\).
---
**Problem Statement**
List the following derivatives in ascending order (lowest to highest):
a) \(g'(-3)\)
b) \(g'(-2)\)
c) \(g'(-1)\)
d) \(g'(2)\)
**_Write your answer as a, d, c, b or b, d, a, c, etc._**
**Answer Box:**
---
**Graph Analysis for Derivatives:**
To determine the derivatives \(g'(x)\) at the given points, consider the slope of the tangent to the curve at those points:
- **\(g'(-3)\)**: The slope here is negative, as the curve descends.
- **\(g'(-2)\)**: The slope is zero, as the curve reaches a trough or flat point.
- **\(g'(-1)\)**: The slope here will be positive, as the curvature starts ascending.
- **\(g'(2)\)**: The slope will be positive and likely constant as the curve forms a linear shape.
### Derivatives Evaluation:
- \(g'(-3)\): Negative slope.
- \(g'(-2)\): Zero slope.
- \(g'(-1)\): Positive slope.
- \(g'(2)\): Positive slope (likely higher than at \(x = -1\)).
By visually analyzing the slopes:
- **Order from lowest to highest slope:**
- Most negative: \(g'(-3)\)
- Zero: \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f9fd18b-deb1-4803-b8c3-1d86990d4df6%2F700c1020-043a-46aa-a489-b77883a636e9%2F5efcu1o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Consider the graph of \( y = g(x) \).**
![Graph]
The graph depicts the function \( g(x) \) and includes the following points of interest:
- X-axis ranges from \(-4\) to \(4\).
- Y-axis ranges from \(-2\) to \(2\).
### Key Plot Points:
- The curve starts at approximately \(( -4, 0.5 )\), reaches a peak just above \(1\) at around \(x = -3\), and then descends crossing the x-axis between \(-2\) and \(-1\).
- The curve reaches its lowest point just below \(-1\) at about \(x = -1\), then ascends, crossing the x-axis again around \(x = 1\).
- The graph appears to linearly increase from \(x = 2\) onward past \(y = 1\).
---
**Problem Statement**
List the following derivatives in ascending order (lowest to highest):
a) \(g'(-3)\)
b) \(g'(-2)\)
c) \(g'(-1)\)
d) \(g'(2)\)
**_Write your answer as a, d, c, b or b, d, a, c, etc._**
**Answer Box:**
---
**Graph Analysis for Derivatives:**
To determine the derivatives \(g'(x)\) at the given points, consider the slope of the tangent to the curve at those points:
- **\(g'(-3)\)**: The slope here is negative, as the curve descends.
- **\(g'(-2)\)**: The slope is zero, as the curve reaches a trough or flat point.
- **\(g'(-1)\)**: The slope here will be positive, as the curvature starts ascending.
- **\(g'(2)\)**: The slope will be positive and likely constant as the curve forms a linear shape.
### Derivatives Evaluation:
- \(g'(-3)\): Negative slope.
- \(g'(-2)\): Zero slope.
- \(g'(-1)\): Positive slope.
- \(g'(2)\): Positive slope (likely higher than at \(x = -1\)).
By visually analyzing the slopes:
- **Order from lowest to highest slope:**
- Most negative: \(g'(-3)\)
- Zero: \(
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