Part CCSIR NET December 2024the-corner-slopes-cap-the-reachable-endpoint

The corner slopes cap the reachable endpoint

For any $b \in R$ , let S(b) denote the set of all broken extremals with one corner of the variational problem: minimize $J [y] = \int_{0}^{1} ((y^{'})^{4} - 3 (y^{'})^{2})$ dx, subject to y(0) = 0, y(1) = b. Then which of the following statements are true?

A.S(2) has exactly two elements
B.S(1/2) has exactly one element
C.S(2) is empty✓
D.S(1/2) has exactly two elements✓

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

The corner slopes cap the reachable endpoint

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