Find $a$ and $b$ so that $f(x)$ below is continuous and differentiable at $x = 1$.

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