Mathematics · Multivariable Calculus
एक फलन f: &mathbb;n → &mathbb; अवतल (CONCAVE) होता है यदि और केवल यदि:
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- 1इसका कोई सैडल बिंदु (saddle point) न हो
- 2इसके प्रथम-क्रम के आंशिक अवकलज (partial derivatives) सभी धनात्मक हों
- 3इसका हेशियन आव्यूह (Hessian matrix) सर्वत्र ऋणात्मक अर्ध-निश्चित (negative semi-definite) हो✓
- 4इसका हेशियन आव्यूह (Hessian matrix) सर्वत्र धनात्मक अर्ध-निश्चित (positive semi-definite) हो
सही उत्तर देखें
इसका हेशियन आव्यूह (Hessian matrix) सर्वत्र ऋणात्मक अर्ध-निश्चित (negative semi-definite) हो
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