A curve has equation

\( y=3x^{-\frac12}-2x^{-\frac32} \).

The curve has a single stationary point when \(x=k\), where \(k>0\).

(a) Find the value of \(k\).

(b) Find \( \frac{d^2y}{dx^2} \), and hence determine whether the stationary point is a maximum or a minimum.

(c) Find the area enclosed by the curve, the \(x\)-axis and the lines \(x=k\) and \(x=4\). Give your answer in the form \(a+b\sqrt c\), where \(a\), \(b\) and \(c\) are integers to be found.