2. (a) Find, in terms of \(a\), the first 3 terms, in ascending powers of \(x\), of the binomial expansion of $$( 2 + a x ) ^ { 6 }$$ where \(a\) is a non-zero constant. Give each term in simplest form. $$f ( x ) = \left( 3 + \frac { 1 } { x } \right) ^ { 2 } ( 2 + a x ) ^ { 6 }$$ Given that the constant term in the expansion of \(\mathrm { f } ( x )\) is 576
(b) find the value of \(a\). \section*{3. In this question you must show all stages of your working.} \section*{Solutions relying entirely on calculator technology are not acceptable.} The curve \(C\) has equation $$y = 4 x ^ { \frac { 1 } { 2 } } + 9 x ^ { - \frac { 1 } { 2 } } + 3 \quad x > 0$$ (a) Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) giving each term in simplest form.
(b) Hence find the \(x\) coordinate of the stationary point of \(C\).
(c) Determine the nature of the stationary point of \(C\), giving a reason for your answer.
(d) State the range of values of \(x\) for which \(y\) is decreasing.
(Total for Question 3 is 7 marks)