Mathematics · Calculus of Variations
For a, b, c ∈ ℝ, consider the variational problem: Minimize J[y] = ∫01 [a(y')2 + 2byy' + cy2] dx subject to y(0) = 10, y(1) = 100. Then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If (a, b, c) = (1, -2, -5), then every admissible extremal is a minimizer
- 2If (a, b, c) = (-1, -1, 1), then every admissible extremal is a minimizer
- 3If (a, b, c) = (1, 0, 2), then every admissible extremal is a minimizer✓
- 4If (a, b, c) = (-2, 1, -2), then every admissible extremal is a minimizer
Correct answer
If (a, b, c) = (1, 0, 2), then every admissible extremal is a minimizer
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