Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question

Help please. I do not really understand this practice question 

The graph depicted is a piecewise function with various segments, including linear and curved parts. It features points and segments of interest: 1. A cusp appears at \(x = -3\). 2. A gap or jump in the graph at \(x = 1\), indicated by an open circle at \((1, 2)\) and a closed circle at \((1, 4)\). Task: - **Select all the points at which the graph is not differentiable:** - [ ] -4 - [x] -3 - [ ] -2 - [ ] -1 - [ ] 0 - [x] 1 - [ ] 2 - [ ] 3 - [ ] 4 The points where the graph is not differentiable are typically those with cusps, corners, or discontinuities.
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Transcribed Image Text:The graph depicted is a piecewise function with various segments, including linear and curved parts. It features points and segments of interest: 1. A cusp appears at \(x = -3\). 2. A gap or jump in the graph at \(x = 1\), indicated by an open circle at \((1, 2)\) and a closed circle at \((1, 4)\). Task: - **Select all the points at which the graph is not differentiable:** - [ ] -4 - [x] -3 - [ ] -2 - [ ] -1 - [ ] 0 - [x] 1 - [ ] 2 - [ ] 3 - [ ] 4 The points where the graph is not differentiable are typically those with cusps, corners, or discontinuities.
Expert Solution
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Step 1: concept

A function is non-differentiable when there is a corner point in its graph.


If the function is not continuous then it is not differentiable, i.e. when there is a gap or a jump in the graph of the function then it is not continuous hence not differentiable.

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