A curve has equation \(y = \frac{1}{k}x^{\frac{1}{2}} + x^{-\frac{1}{2}} + \frac{1}{k^2}\) where \(x > 0\) and \(k\) is a positive constant.

It is given that when \(x = \frac{1}{4}\), the gradient of the curve is 3.

Find the value of \(k\).