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The graph off' (not f) is given below. x1 x2 x3 x4 x5 x6 (Note that this is a graph of f', not a graph of f.)

The graph off' (not f) is given below. x1 x2 x3 x4 x5 x6 (Note that this is a graph of f', not a graph of f.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please help answer thank you in advance. both pictures are one question, thank you 

### Graph of \( f' \) (Derivative of \( f \)) #### Description: The graph above represents the derivative of a function \( f \), denoted as \( f' \). #### Key Points: - **Axes and Scale:** The graph is plotted on a Cartesian plane without specific numerical values on the axes. The x-axis has marked points at \( x_1, x_2, x_3, x_4, x_5, \) and \( x_6 \). - **Graph Characteristics:** - The curve begins at a low point and rises to a peak just before \( x_2 \). - It descends to a lower peak between \( x_2 \) and \( x_3 \). - The graph then ascends again, peaking at a point just before \( x_5 \). - Finally, it descends steeply towards \( x_6 \). - **Behavior:** - At each marked point on the x-axis, there are vertically dashed lines indicating significant points or transitions in the slope behavior. - The graph is smooth and continuous, suggesting the function \( f \) is differentiable over the interval shown. #### Note: This is a graph of the derivative \( f' \), which illustrates the rate of change of the original function \( f \). It is important not to confuse this with a graph of \( f \) itself.
Transcribed Image Text:### Graph of \( f' \) (Derivative of \( f \)) #### Description: The graph above represents the derivative of a function \( f \), denoted as \( f' \). #### Key Points: - **Axes and Scale:** The graph is plotted on a Cartesian plane without specific numerical values on the axes. The x-axis has marked points at \( x_1, x_2, x_3, x_4, x_5, \) and \( x_6 \). - **Graph Characteristics:** - The curve begins at a low point and rises to a peak just before \( x_2 \). - It descends to a lower peak between \( x_2 \) and \( x_3 \). - The graph then ascends again, peaking at a point just before \( x_5 \). - Finally, it descends steeply towards \( x_6 \). - **Behavior:** - At each marked point on the x-axis, there are vertically dashed lines indicating significant points or transitions in the slope behavior. - The graph is smooth and continuous, suggesting the function \( f \) is differentiable over the interval shown. #### Note: This is a graph of the derivative \( f' \), which illustrates the rate of change of the original function \( f \). It is important not to confuse this with a graph of \( f \) itself.
Certainly! Here is the transcribed text: --- **At which of the marked values of x is** A. \( f(x) \) greatest? \( x = \) [ ] B. \( f(x) \) least? \( x = \) [ ] C. \( f'(x) \) greatest? \( x = \) [ ] D. \( f'(x) \) least? \( x = \) [ ] E. \( f''(x) \) greatest? \( x = \) [ ] F. \( f''(x) \) least? \( x = \) [ ] --- This section seems to be part of a calculus lesson focusing on identifying the maximum and minimum values of a function and its derivatives at specific marked points along the x-axis.
Transcribed Image Text:Certainly! Here is the transcribed text: --- **At which of the marked values of x is** A. \( f(x) \) greatest? \( x = \) [ ] B. \( f(x) \) least? \( x = \) [ ] C. \( f'(x) \) greatest? \( x = \) [ ] D. \( f'(x) \) least? \( x = \) [ ] E. \( f''(x) \) greatest? \( x = \) [ ] F. \( f''(x) \) least? \( x = \) [ ] --- This section seems to be part of a calculus lesson focusing on identifying the maximum and minimum values of a function and its derivatives at specific marked points along the x-axis.
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