For each of the graphs below, put a box around (the entire graph of) any graph that is differentiable (on the axes shown). If a graph is not differentiable, circle the location(s) on the graph that are not differentiable. If you need to, carefully re-draw the graphs below on a piece of paper to answer this question. 15 1 0.5 0 -05 05 15 2 2
For each of the graphs below, put a box around (the entire graph of) any graph that is differentiable (on the axes shown). If a graph is not differentiable, circle the location(s) on the graph that are not differentiable. If you need to, carefully re-draw the graphs below on a piece of paper to answer this question. 15 1 0.5 0 -05 05 15 2 2
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section: Chapter Questions
Problem 74SGR
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![### Differentiability of Graphs
In this section, we'll examine various graphs to determine whether they are differentiable. We'll put a box around the entire graph of any differentiable graph and circle the points of non-differentiability for those that are not differentiable.
#### Graph Descriptions
1. **Top Left Graph (Red Curve)**:
- The graph is a smooth, continuous curve with no sharp corners or discontinuities. It appears to be differentiable everywhere.
2. **Top Middle Graph (Orange Line)**:
- The graph is a straight line with a constant slope. Since there are no discontinuities or sharp corners, it’s differentiable everywhere.
3. **Top Right Graph (Blue V-Shaped Curve)**:
- The graph consists of straight line segments joined at points with sharp corners. These points of sharp corners are where the graph is not differentiable.
4. **Middle Left Graph (Purple Curve)**:
- Similar to the top left red curve, this graph is smooth and continuous, with no regions of non-differentiability.
5. **Middle Right Graph (Blue Angular Function)**:
- The graph is made up of multiple linear segments, and there are sharp changes in direction at the points where these segments meet. These points are not differentiable.
6. **Bottom Left Graph (Green Curve)**:
- The graph shows a smooth, continuous curve without any sharp corners or cusps. Hence, it is differentiable everywhere.
7. **Bottom Right Graph (Red V-Shaped Curve)**:
- This graph features a sharp point at the peak of the curve. This point is where the graph is not differentiable.
### Instructions for Assessment
- **Box the entire graph** if it is differentiable everywhere.
- **Circle the points** on the graph that are not differentiable.
### Graph Analysis
1. **Red Curve (Top Left)**:
- Box around the entire graph
- Differentiable everywhere
2. **Orange Line (Top Middle)**:
- Box around the entire graph
- Differentiable everywhere
3. **Blue Angular Line (Top Right)**:
- Circle at each point where the slope sharply changes direction
- Not differentiable at the sharp points where the line segments meet
4. **Purple Curve (Middle Left)**:
- Box around the entire graph
- Differentiable everywhere
5. **Blue](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F114d112a-89da-40ea-8ec8-a25f26317aff%2F54d2c73f-01bf-4422-b31d-052e1c0eaa1f%2Fddxj93q_processed.png&w=3840&q=75)
Transcribed Image Text:### Differentiability of Graphs
In this section, we'll examine various graphs to determine whether they are differentiable. We'll put a box around the entire graph of any differentiable graph and circle the points of non-differentiability for those that are not differentiable.
#### Graph Descriptions
1. **Top Left Graph (Red Curve)**:
- The graph is a smooth, continuous curve with no sharp corners or discontinuities. It appears to be differentiable everywhere.
2. **Top Middle Graph (Orange Line)**:
- The graph is a straight line with a constant slope. Since there are no discontinuities or sharp corners, it’s differentiable everywhere.
3. **Top Right Graph (Blue V-Shaped Curve)**:
- The graph consists of straight line segments joined at points with sharp corners. These points of sharp corners are where the graph is not differentiable.
4. **Middle Left Graph (Purple Curve)**:
- Similar to the top left red curve, this graph is smooth and continuous, with no regions of non-differentiability.
5. **Middle Right Graph (Blue Angular Function)**:
- The graph is made up of multiple linear segments, and there are sharp changes in direction at the points where these segments meet. These points are not differentiable.
6. **Bottom Left Graph (Green Curve)**:
- The graph shows a smooth, continuous curve without any sharp corners or cusps. Hence, it is differentiable everywhere.
7. **Bottom Right Graph (Red V-Shaped Curve)**:
- This graph features a sharp point at the peak of the curve. This point is where the graph is not differentiable.
### Instructions for Assessment
- **Box the entire graph** if it is differentiable everywhere.
- **Circle the points** on the graph that are not differentiable.
### Graph Analysis
1. **Red Curve (Top Left)**:
- Box around the entire graph
- Differentiable everywhere
2. **Orange Line (Top Middle)**:
- Box around the entire graph
- Differentiable everywhere
3. **Blue Angular Line (Top Right)**:
- Circle at each point where the slope sharply changes direction
- Not differentiable at the sharp points where the line segments meet
4. **Purple Curve (Middle Left)**:
- Box around the entire graph
- Differentiable everywhere
5. **Blue
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