Mathematics · Calculus of Variations
a, b, c ∈ ℝ के लिए, विचरण समस्या (variational problem) पर विचार करें: y(0) = 10, y(1) = 100 के अधीन J[y] = ∫01 [a(y')2 + 2byy' + cy2] dx को न्यूनतम करें। तो निम्नलिखित में से कौन सा कथन सत्य है?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1यदि (a, b, c) = (1, -2, -5) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता (minimizer) है
- 2यदि (a, b, c) = (-1, -1, 1) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता (minimizer) है
- 3यदि (a, b, c) = (1, 0, 2) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता (minimizer) है✓
- 4यदि (a, b, c) = (-2, 1, -2) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता (minimizer) है
सही उत्तर देखें
यदि (a, b, c) = (1, 0, 2) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता (minimizer) है
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