16. Consider F(y) = f'¹[(y')² + ry' ]e−²y dx where y(0) = 1, y(1) is free, and r is a constant. Find the extremals. Show there are no extremals if r ≥ r#, and only one extremal if r < r#, where r# is a number that you should find.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 45E
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16. Consider F(y) = · S'[(v')² + ry' ]e−²y dx where y(0) = 1, y(1) is free, and r is a
constant. Find the extremals. Show there are no extremals if r ≥ r#, and only one
extremal if r < r#,
where r# is a number that you should find.
Transcribed Image Text:16. Consider F(y) = · S'[(v')² + ry' ]e−²y dx where y(0) = 1, y(1) is free, and r is a constant. Find the extremals. Show there are no extremals if r ≥ r#, and only one extremal if r < r#, where r# is a number that you should find.
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Calculus For The Life Sciences
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,