4 The equation of a curve is \(y = f ( x )\), where \(f ( x ) = ( 2 x - 1 ) \sqrt { 3 x - 2 } - 2\). The following points lie on the curve. Non-exact values have been given correct to 5 decimal places. $$A ( 2,4 ) , B ( 2.0001 , k ) , C ( 2.001,4.00625 ) , D ( 2.01,4.06261 ) , E ( 2.1,4.63566 ) , F ( 3,11.22876 )$$

1. Find the value of \(k\). Give your answer correct to 5 decimal places.
   The table shows the gradients of the chords \(A B , A C , A D\) and \(A F\).

   Chord	\(A B\)	\(A C\)	\(A D\)	\(A E\)	\(A F\)
   Gradient of chord	6.2501	6.2511	6.2608		7.2288

2. Find the gradient of the chord \(A E\). Give your answer correct to 4 decimal places.
3. Deduce the value of \(f ^ { \prime } ( 2 )\) using the values in the table.