For any two positive numbers a and x, least value of $$ax+\frac ax$$ is​

Correct option is D

​$$\textbf{Given:} \\f(x) = ax + \frac{a}{x}, \quad \text{where } a > 0 \text{ and } x > 0\\[10pt]\textbf{Formula:} \\\text{Use the inequality: } \text{AM} \geq \text{GM} \\\ \\\Rightarrow \frac{ax + \frac{a}{x}}{2} \geq \sqrt{ax \cdot \frac{a}{x}} \\\ \\\Rightarrow ax + \frac{a}{x} \geq 2\sqrt{a^2} = 2a\\[10pt]\textbf{Solution:} \\\text{Equality holds when } ax = \frac{a}{x} \Rightarrow x^2 = 1 \Rightarrow x = 1 \\\ \\\text{At } x = 1, \quad f(x) = a(1) + \frac{a}{1} = 2a\\[10pt]\textbf{Final Answer:} \\\boxed{2a}$$

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