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If \(f(x)=10-(x+2)^2\), what is the maximum value of \(f(x)\)?यदि \(f(x)=10-(x+2)^2\), तो \(f(x)\) का अधिकतम मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(10\)\(10\)
\((x+2)^2\ge 0\) for all real \(x\). Since \(f(x)=10-(x+2)^2\), subtracting a nonnegative quantity from \(10\) makes \(f(x)\le 10\). The maximum happens when \((x+2)^2=0\Rightarrow x=-2\). Then \(f(-2)=10-0=10\).सभी वास्तविक \(x\) के लिए \((x+2)^2\ge 0\) होता है। क्योंकि \(f(x)=10-(x+2)^2\), इसलिए \(10\) में से किसी अशून्य (nonnegative) मात्रा को घटाने पर \(f(x)\le 10\) रहेगा। अधिकतम मान तब होगा जब \((x+2)^2=0\Rightarrow x=-2\)। तब \(f(-2)=10-0=10\).
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