Part CCSIR NET June 2024satisfying-the-constraints-is-not-being-an-extremal

Satisfying the constraints is not being an extremal

The extremizer of the problem $min [(1/2) \int$ ₋ $_{1}^{1} ((y^{'} (x))^{2} + (y (x))^{2})$ dx] subject to $y \in C^{1} [- 1, 1], \int$ ₋ $_{1}^{1}$ xy(x)dx = 0 and y(−1) = y(1) = 1 is

A. $(e / (1 + e^{2})) (e$ ˣ + e⁻ˣ $) + x^{2} - 1$
B. $(e / (1 + e^{2})) (e$ ˣ + e⁻ˣ $) + 1 - x^{2}$
C. $(e / (1 + e^{2})) (e$ ˣ + e⁻ˣ)✓
D. $(e / (1 + e^{2})) (e$ ˣ + e⁻ˣ $) + sin (2 π x)$

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.

Satisfying the constraints is not being an extremal

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