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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

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...
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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
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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