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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+2x+2), what is the minimum value?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+2x+2), तो न्यूनतम मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1)(1)
Step 1: (x^2+2x+2=(x+1)^2+1). Step 2: Since ((x+1)^2\ge 0), the smallest value is (1). Step 3: Completing the square quickly gives range and minimum value.चरण 1: (x^2+2x+2=(x+1)^2+1)। चरण 2: ((x+1)^2\ge 0), इसलिए सबसे छोटा मान (1) है। चरण 3: वर्ग पूर्ण करने से परास और न्यूनतम मान जल्दी मिलते हैं।
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