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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Question
![### Critical Points Identification from a Graph
#### Problem Statement
**2.** List (by letter) all Critical Points from the graph below.
#### Graph Description
The graph provided is a plot with an undulating curve characterized by several peaks and valleys, representative of a function with multiple turning points. The graph features:
- **Axes:** The horizontal axis represents the variable with markers labeled A through H. The vertical axis indicates function values with grid lines for reference.
- **Curve:** A dashed line indicates the path of the function across the chart.
#### Critical Points
Critical points on the graph are where the slope of the curve is zero (horizontal tangent) or undefined. These typically occur at the peaks and valleys where the function changes direction. The critical points in the graph are:
- **Point B:** This is a local maximum where the curve reaches a peak before descending.
- **Point D:** This is a local minimum where the curve reaches a valley before ascending.
- **Point F:** This is another local maximum, with the curve peaking before descending again.
- **Point H:** This is the highest maximum on the graph, where the curve is rising steeply.
#### Solution
Identify the corresponding letters of the critical points (B, D, F, H) and explain their significance in the analysis of the function.
**Answer: B, D, F, H**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1ba6bbb-fc76-4ff1-897e-f936bd2be4a6%2F70902108-7c24-4e4b-b13b-75103106d688%2Fwj5k31t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Critical Points Identification from a Graph
#### Problem Statement
**2.** List (by letter) all Critical Points from the graph below.
#### Graph Description
The graph provided is a plot with an undulating curve characterized by several peaks and valleys, representative of a function with multiple turning points. The graph features:
- **Axes:** The horizontal axis represents the variable with markers labeled A through H. The vertical axis indicates function values with grid lines for reference.
- **Curve:** A dashed line indicates the path of the function across the chart.
#### Critical Points
Critical points on the graph are where the slope of the curve is zero (horizontal tangent) or undefined. These typically occur at the peaks and valleys where the function changes direction. The critical points in the graph are:
- **Point B:** This is a local maximum where the curve reaches a peak before descending.
- **Point D:** This is a local minimum where the curve reaches a valley before ascending.
- **Point F:** This is another local maximum, with the curve peaking before descending again.
- **Point H:** This is the highest maximum on the graph, where the curve is rising steeply.
#### Solution
Identify the corresponding letters of the critical points (B, D, F, H) and explain their significance in the analysis of the function.
**Answer: B, D, F, H**
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