3 The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = x ^ { 3 } + p x + q\), where \(p\) and \(q\) are constants.
- Given that \(\mathrm { f } ^ { \prime } ( 2 ) = 13\), find the value of \(p\).
- Given also that ( \(x - 2\) ) is a factor of \(\mathrm { f } ( x )\), find the value of \(q\).
The curve \(y = \mathrm { f } ( x )\) is translated by the vector \(\binom { 2 } { - 3 }\).
- Using the values from part (a), determine the equation of the curve after it has been translated. Give your answer in the form \(y = x ^ { 3 } + a x ^ { 2 } + b x + c\), where \(a , b\) and \(c\) are integers to be found.