10 The equation of a curve is \(y = x ^ { 2 } - 3 x + 4\).
- Show that the whole of the curve lies above the \(x\)-axis.
- Find the set of values of \(x\) for which \(x ^ { 2 } - 3 x + 4\) is a decreasing function of \(x\).
The equation of a line is \(y + 2 x = k\), where \(k\) is a constant.
- In the case where \(k = 6\), find the coordinates of the points of intersection of the line and the curve.
- Find the value of \(k\) for which the line is a tangent to the curve.