Mathematics · Calculus of Variations
a, b, c ∈ ℝ के लिए, विचरण समस्या (variational problem): Minimize J[y] = ∫02 [a(y')2 + 2byy' + cy2] dx जबकि y(0)=10, y(1)=100 है, पर विचार 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 है✓
- 2यदि (a, b, c) = (-1, 2, -5) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता है
- 3यदि (a, b, c) = (0, 1, 2) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता है
- 4यदि (a, b, c) = (-2, 1, -2) है, तो प्रत्येक स्वीकार्य चरम (admissible extremal) एक न्यूनतमकर्ता (minimizer) है
सही उत्तर देखें
यदि (a, b, c) = (1, -2, 5) है, तो प्रत्येक स्वीकार्य चरम एक न्यूनतमकर्ता है
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