Mathematics · Calculus of Variations
For any b ∈ ℝ, let S(b) denote the set of all broken extremals with exactly one corner for the variational problem: minimize J[y] = ∫01 ((y')4 - 3(y')2) dx subject to y(0) = 0, y(1) = b. Then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1S(2) has exactly two elements.
- 2S(12) has exactly one element.
- 3S(2) is empty.
- 4S(12) has exactly two elements.✓
Correct answer
S(12) has exactly two elements.
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