3 The diagram shows a curve with a maximum point \(M\).
\includegraphics[max width=\textwidth, alt={}, center]{e183578a-29a8-4112-b941-06c8894ed078-06_512_867_354_589}
The curve is defined for \(x > 0\) by the equation
$$y = 6 x ^ { \frac { 1 } { 2 } } - x - 3$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Hence find the \(y\)-coordinate of the maximum point \(M\).
- Find an equation of the normal to the curve at the point \(P ( 4,5 )\).
- It is given that the normal to the curve at \(P\), when translated by the vector \(\left[ \begin{array} { l } k
0 \end{array} \right]\), passes through the point \(M\). Find the value of the constant \(k\).
[0pt]
[3 marks]