For $f(x)$ below, find the values of $a$ and $b$ such that $f(x)$ is both continuous and differentiable for all values of $x$. Justify your answer.

$f ( x ) = \left\{ \begin{array} { l l } { a x ^ { 2 } } & { \text { for } x \leq 1 } \\ { b x + 2 } & { \text { for } x > 1 } \end{array} \right.$