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Consider the graph y -6- nction shown. Use the -5 e on p. 143 to list all x- which the derivative nction fails to exist. -10 such x-value, give the -9 -8 -7 -6 -5 -4 -3 -2 4 6. eason why the -3 s not differentiable. -5

Consider the graph y -6- nction shown. Use the -5 e on p. 143 to list all x- which the derivative nction fails to exist. -10 such x-value, give the -9 -8 -7 -6 -5 -4 -3 -2 4 6. eason why the -3 s not differentiable. -5

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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**Transcription for Educational Website:** --- **Title: Understanding Differentiability in Graphs** **Task:** Consider the graph of the function shown. Use the guidance on p. 143 to list all x-values at which the derivative of this function fails to exist. For each such x-value give the specific reason why the function is not differentiable. **Graph Explanation:** The graph provided is a plotted line graph, represented on a coordinate plane with x and y axes. Several critical points and features are visible: 1. **Points and Intervals:** - The graph includes plotted points and line segments. - There appears to be a discontinuity or sharp corner at some points. - The line is continuous in sections but has breaks or jumps. 2. **Differentiability Issues:** - At specific x-values, there might be points where the derivative does not exist, typically due to sharp corners, vertical tangents, or discontinuities. 3. **Observations:** - Near the x-values 0, 2, and 3, consider areas where the function is not smooth. - At these points, evaluate whether the graph has sharp turns or breaks, indicating non-differentiability. **Analysis:** This exercise will help you determine where a function lacks differentiability by analyzing sharp turns or discontinuities on its graph. Reflect on the graph's features, keeping in mind that a function is not differentiable at a point if it is not continuous there, if there is a sharp corner or cusp, or if there is a vertical tangent line at the point. ---
Transcribed Image Text:**Transcription for Educational Website:** --- **Title: Understanding Differentiability in Graphs** **Task:** Consider the graph of the function shown. Use the guidance on p. 143 to list all x-values at which the derivative of this function fails to exist. For each such x-value give the specific reason why the function is not differentiable. **Graph Explanation:** The graph provided is a plotted line graph, represented on a coordinate plane with x and y axes. Several critical points and features are visible: 1. **Points and Intervals:** - The graph includes plotted points and line segments. - There appears to be a discontinuity or sharp corner at some points. - The line is continuous in sections but has breaks or jumps. 2. **Differentiability Issues:** - At specific x-values, there might be points where the derivative does not exist, typically due to sharp corners, vertical tangents, or discontinuities. 3. **Observations:** - Near the x-values 0, 2, and 3, consider areas where the function is not smooth. - At these points, evaluate whether the graph has sharp turns or breaks, indicating non-differentiability. **Analysis:** This exercise will help you determine where a function lacks differentiability by analyzing sharp turns or discontinuities on its graph. Reflect on the graph's features, keeping in mind that a function is not differentiable at a point if it is not continuous there, if there is a sharp corner or cusp, or if there is a vertical tangent line at the point. ---
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