Given that \(\frac { 4 x ^ { 3 } - 2 x ^ { 2 } + 16 x - 3 } { 2 x ^ { 2 } - x + 2 }\) can be expressed as \(A x + \frac { B ( 4 x - 1 ) } { 2 x ^ { 2 } - x + 2 }\), find the values of the constants \(A\) and \(B\).
The gradient of a curve is given by
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 x ^ { 3 } - 2 x ^ { 2 } + 16 x - 3 } { 2 x ^ { 2 } - x + 2 }$$
The point \(( - 1,2 )\) lies on the curve. Find the equation of the curve. [0pt]
[4 marks]