It is given that \(y = x ^ { 2 } + 3 x\).
(a) Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
(b) Find the values of \(x\) for which \(y\) is increasing.
Find \(\int ( 3 - 4 \sqrt { x } ) \mathrm { d } x\).
\(5 N\) is an integer that is not divisible by 3 . Prove that \(N ^ { 2 }\) is of the form \(3 p + 1\), where \(p\) is an integer.