11 The equation of a curve is
$$y = k \sqrt { 4 x + 1 } - x + 5$$
where \(k\) is a positive constant.
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Find the \(x\)-coordinate of the stationary point in terms of \(k\).
- Given that \(k = 10.5\), find the equation of the normal to the curve at the point where the tangent to the curve makes an angle of \(\tan ^ { - 1 } ( 2 )\) with the positive \(x\)-axis.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.