Part CCSIR NET December 2024free-endpoints-give-the-total-derivative-term-teeth

Free endpoints give the total derivative term teeth

Consider the variational problem minimize $J [y] = \int_{0}^{1} [(y^{'})^{2} + 2025$ yy′]dx, where y(0) and y(1) are free. Then which of the following statements are true?

A.There are infinitely many extremals
B.There are more than one but only finitely many extremals
C.There is no extremal
D.There is a unique extremal✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: A weak minimum of a functional is a strong minimum

Free endpoints give the total derivative term teeth

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