At the point (4, -1) on a curve, the gradient of the curve is \(-\frac{3}{2}\). It is given that \(\frac{dy}{dx} = x^{-\frac{1}{2}} + k\), where \(k\) is a constant.

(a) Show that \(k = -2\).

(b) Find the equation of the curve.

(c) Find the coordinates of the stationary point.

(d) Determine the nature of the stationary point.