Given that $\displaystyle f(x) = x^{-\sqrt x}$ for $\displaystyle x > 0$,

(a) obtain an expression for f′ (x), [4]

(b) find the x-coordinate of the stationary point on the graph of f and determine whether this point is a maximum or a minimum. [4]

Now for the first part, I obtained a derivative of

$\displaystyle (x^{-\sqrt x}) \frac{-1}{\sqrt x} - \frac{lnx}{2\sqrt x}$ through logarithmic differentiation. I think this is correct, but the problem I have is knowing what to do in the second part of the question. How would you go about finding the x-coordinate and how can you tell what kind of point it is?

Thanks again for your time and patience