### Explanation of GraphsThis image presents the graphs of three functions labeled $ f $, $ g $, and $ h $. Each function is represented by a different colored curve:- **Function $ f $**: Represented by a blue curve, which is monotonically increasing over the displayed range.- **Function $ g $**: Represented by an orange curve, displaying a downward-opening parabolic shape that reaches a maximum around $ x = 0 $.- **Function $ h $**: Represented by a green curve, showing an upward-opening parabolic shape with a minimum around $ x = 0 $.The graph is plotted with the x-axis ranging from -2 to 2, and the y-axis from -1 to 1.### Analytical ObservationsThe functions' behavior suggests the following relationships:- The curve $ g $ could represent the first derivative of $ f $, as it is consistent with $ f $ showing increasing behavior with a change in curvature.- The curve $ h $ might represent the second derivative of $ f $, given that it indicates curvature changes at its peak and trough.### Matching StatementsThe goal is to determine which of the given statements best describes the relationships between the graphs of $ f $, $ g $, and $ h $:- $ f' = g $ and $ f'' = h $- $ f' = h $ and $ f'' = g $- $ g' = h $ and $ g'' = f $- $ h' = g $ and $ h'' = f $### Correct AnswerBased on the observed characteristics of the functions, the statement that appears consistent with the graphs is:- $ f' = g $ and $ f'' = h $This choice assumes standard characteristics of derivatives, where $ f' $ describes the local slopes of $ f $, and $ f'' $ the concavity.

Answered: Image /qna-images/answer/2ab64ab7-1ca4-42a0-ab1c-7fdefb4c1532.jpg

Answered: 1.0 0.5 g -2 -1 1 2 h -0.5

1.0 0.5 g -2 -1 1 2 h -0.5

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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