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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)∫\min[(1/2)\int₋11((y′(x))2+(y(x))2)_{1}^{1} ((y'(x))^{2} + (y(x))^{2})dx] subject to y∈C1[−1,1],∫y \in C^{1}[-1, 1], \int₋11_{1}^{1} xy(x)dx = 0 and y(−1) = y(1) = 1 is

  1. A.(e/(1+e2))(e(e/(1 + e^{2}))(eˣ + e⁻ˣ)+x2−1) + x^{2} - 1
  2. B.(e/(1+e2))(e(e/(1 + e^{2}))(eˣ + e⁻ˣ)+1−x2) + 1 - x^{2}
  3. C.(e/(1+e2))(e(e/(1 + e^{2}))(eˣ + e⁻ˣ)✓ Correct
  4. D.(e/(1+e2))(e(e/(1 + e^{2}))(eˣ + e⁻ˣ)+sin⁡(2πx)) + \sin(2\pi{}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, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

More on this topic

The chapter behind this: Constrained variational problems — free to read

From Calculus of Variations › Isoperimetric problems

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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