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What is the minimum value of the function \(f(x)=\sqrt{x}+4\), where \(x\ge 0\)?फलन \(f(x)=\sqrt{x}+4\), जहाँ \(x\ge 0\), का न्यूनतम मान क्या है?
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Correct answer:सही उत्तर: 44
A square root is always non-negative, so \(\sqrt{x}\ge 0\). Therefore, \(f(x)=\sqrt{x}+4\ge 4\). At \(x=0\), \(f(0)=4\), so the minimum value is 4. The value 0 is the minimum of \(\sqrt{x}\) alone, not of the whole function. Exam tip: For a square-root function, first use the fact that the square-root term is at least zero.वर्गमूल का मान सदैव गैर-ऋणात्मक होता है, इसलिए \(\sqrt{x}\ge 0\)। अतः \(f(x)=\sqrt{x}+4\ge 4\)। जब \(x=0\), तब \(f(0)=4\), इसलिए न्यूनतम मान 4 है। विकल्प 0 केवल \(\sqrt{x}\) का न्यूनतम मान है, पूरे फलन का नहीं। परीक्षा-युक्ति: वर्गमूल वाले फलन में पहले \(\sqrt{x}\ge 0\) का उपयोग करें।
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