Differentiation - Connected Rates of Change

A curve has the equation \(y = x^3 + 4x^2 + kx + 3\), where \(k\) is a constant. Find, respectively, the range of values of \(k\) for which

1. the curve is always increasing, and
2. the curve has a stationary point at which \(\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} = 0\).
3. In the case where \(k = 6\), and the rate of increase of \(x\) is \(0.05\) unit/s when \(x = 1\), find the rate of change of \(y\) at this instant.