Applications of Differentiation - Stationary Points and Their Nature

A curve has the equation \(y = 2x^3 - 3x^2 - 36x + m\), where \(m\) is a constant.

1. Find, in terms of \(m\), the coordinates of the point(s) on the curve at which the tangent to the curve is perpendicular to the \(y\)-axis.
2. Hence, or otherwise, find the possible value(s) of \(m\), such that the \(x\)-axis is a tangent to the curve.