The following shows graphs of three functions, A (in black), B (in blue), and C (in green). If these are the graphs of three functions f, f' , and f'' , identify which is which.
The following shows graphs of three functions, A (in black), B (in blue), and C (in green). If these are the graphs of three functions f, f' , and f'' , identify which is which.
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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The following shows graphs of three functions, A (in black), B (in blue), and C (in green). If these are the graphs of three functions f, f' , and f'' , identify which is which.
Transcribed Image Text:The image displays a graph with three different colored curves on a Cartesian plane.
1. **Axis Details**:
- The graph has both x and y axes with a grid backdrop, and the axes intersect at the origin (0,0).
- The grid is divided into quadrants, aiding in visualizing the curves.
2. **Curve Descriptions**:
- **Blue Curve**:
- This curve has a steep upward and downward trajectory with two prominent humps indicating key turning points or critical points.
- It crosses the x-axis at one point in the displayed section.
- **Black Curve**:
- This curve has a smoother and broader peak than the blue curve, suggesting a gentler rate of change.
- It also intersects the x-axis, showing at least one real root within the visible part.
- **Green Curve**:
- The green curve is the most gradual, with a slight wave pattern indicating lesser variation compared to the blue and black curves.
- It also appears to intersect the x-axis once within the range shown.
3. **Overall Description**:
- The curves likely represent different mathematical functions, showing varying degrees of complexity and behavior such as multiple turning points and intercepts.
- The visual differences highlight contrasts in growth rates and critical points, useful for comparing polynomial or trigonometric function behavior in mathematics.
These diagrams can be used to teach concepts related to graphing functions, analyzing intercepts, critical points, and the general behavior of mathematical functions.
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