Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Graph of the Derivative of Function \( f \)** The graph depicts the derivative of the function \( f \). Our objective is to determine the \( x \)-coordinates of all stationary and singular points of \( f \), classifying each as a relative maximum, relative minimum, or neither. It is given that \( f(x) \) is defined and continuous throughout the interval \([-18, 18]\). **Graph Analysis:** - The \( y \)-axis represents the value of the derivative \( f'(x) \). - The \( x \)-axis represents the input values for the function. - The graph shows how the derivative behaves across the given interval: - The graph crosses the \( x \)-axis at several points, indicating potential stationary points where the derivative equals zero. **Classification and Points:** 1. **Stationary Non-Extreme Point:** - At \( x = -6 \): The graph indicates a crossing at this point without a change of direction, suggesting a possible inflection point. 2. **Singular Minimum:** - No singular minimum is identified from the graph. 3. **Stationary Maximum:** - No stationary maximum is indicated in the options. **Conclusion:** Based on the graph, the only identified and classified point is a stationary non-extreme point at \( x = -6 \). Other classifications require a change in the direction of the derivative at zero which is not observed here.
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Transcribed Image Text:**Graph of the Derivative of Function \( f \)** The graph depicts the derivative of the function \( f \). Our objective is to determine the \( x \)-coordinates of all stationary and singular points of \( f \), classifying each as a relative maximum, relative minimum, or neither. It is given that \( f(x) \) is defined and continuous throughout the interval \([-18, 18]\). **Graph Analysis:** - The \( y \)-axis represents the value of the derivative \( f'(x) \). - The \( x \)-axis represents the input values for the function. - The graph shows how the derivative behaves across the given interval: - The graph crosses the \( x \)-axis at several points, indicating potential stationary points where the derivative equals zero. **Classification and Points:** 1. **Stationary Non-Extreme Point:** - At \( x = -6 \): The graph indicates a crossing at this point without a change of direction, suggesting a possible inflection point. 2. **Singular Minimum:** - No singular minimum is identified from the graph. 3. **Stationary Maximum:** - No stationary maximum is indicated in the options. **Conclusion:** Based on the graph, the only identified and classified point is a stationary non-extreme point at \( x = -6 \). Other classifications require a change in the direction of the derivative at zero which is not observed here.
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