Show that the maximum value of `(1/x)^x` is `e^(1/e)dot`

Explanation

To find the maximum value of the function \( f(x) = \left( \frac{1}{x} \right)^x \), we can follow these steps:

### Step 1: Rewrite the function
We can rewrite the function in a more manageable form using logarithms. Let:
\[ y = \left( \frac{1}{x} \right)^x \]
Taking the natural logarithm on both sides, we have:
...