(a)[3]
Express $3x^2 - 6x + 2$ as $(x + b)^2 + c$, where $b$ and $c$ are constants.
(b)[3]
The function $f$, given by $f(x) = x^3 - 3x^2 + 7x - 8$, is defined for $x \in \mathbb{R}$. Find $f'(x)$ and state, with a reason, whether $f$ is increasing, decreasing or neither.