JEE Math Practice Question
If the function $$f(x)=\left(\frac{1}{x}\right)^{2 x} ; x>0$$ attains the maximum value at $$x=\frac{1}{\mathrm{e}}$$ then :
- A.$$\mathrm{e}^\pi<\pi^{\mathrm{e}}$$
- B.$$\mathrm{e}^{2 \pi}<(2 \pi)^{\mathrm{e}}$$
- C.$$(2 e)^\pi>\pi^{(2 e)}$$
- D.$$\mathrm{e}^\pi>\pi^{\mathrm{e}}$$
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