Let

1. Find $f^{\prime }(x)$ and $f^{″}(x)$

2. Hence, find the minimum value of $f,$ justifying that this is a minimum point.

Express $f$ in the form

in order to differentiate it

Remember that $\ln (x)$ and $e^x$ are inverse to each other, which means

and

You must use the second derivative test to determine the nature of the turning point.

Give your answer below