7. A curve \(C\) has equation \(y = \mathrm { f } ( x )\).
Given that
- \(\mathrm { f } ^ { \prime } ( x ) = 18 x ^ { 2 } + 2 a x + b\)
- the \(y\)-intercept of \(C\) is - 48
- the point \(A\), with coordinates \(( - 1,45 )\) lies on \(C\)
a. Show that \(a - b = 99\)
b. Find the value of \(a\) and the value of \(b\).
c. Show that \(( 2 x + 1 )\) is a factor of \(\mathrm { f } ( x )\).