Part BCSIR NET December 2024a-total-derivative-term-cannot-affect-the-extremal

A total derivative term cannot affect the extremal

If $φ \in C^{4} [0, 1]$ is the extremal of the variational problem minimize $J [y] = \int_{0}^{1} ($ yy $^{'} + (y^{''})^{2})$ dx, subject to y(0) = 0, y′(0) = 1, y(1) = 2, y′(1) = 4, then $φ (1/2)$ is equal to

A.5/8✓
B.3/4
C.3/8
D.5/4

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

A total derivative term cannot affect the extremal

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