JEE Mains · Maths · STD 12 - 6. Application of derivatives
The minimum value of \(f ( x )= a ^{ a ^{ x }}+ a ^{1- a ^{ x }},\) where \(a, x \in R\) and \(a > 0\), is equal to ..... .
- A \(2 a\)
- B \(2 \sqrt{ a }\)
- C \(a +\frac{1}{ a }\)
- D \(a +1\)
Answer & Solution
Correct Answer
(B) \(2 \sqrt{ a }\)
Step-by-step Solution
Detailed explanation
\(A.M.\) \(\geq\) \(G.M.\) \(f(x)=a^{a^{x}}+a^{1-a^{x}}=a^{a^{x}}+\frac{a}{a^{a^{x}}} \geq 2 \sqrt{a}\)
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