JEE Math Practice Question

If the function f(x) = $$\left\{ {\begin{matrix} { - x} & {x < 1} \\ {a + {{\cos }^{ - 1}}\left( {x + b} \right),} & {1 \le x \le 2} \\ \end{matrix} } \right.$$ is differentiable at x = 1, then $${a \over b}$$ is equal to :

1. A.$${{\pi - 2} \over 2}$$
2. B.$${{ - \pi - 2} \over 2}$$
3. C.$${{\pi + 2} \over 2}$$
4. D.$$ - 1 - {\cos ^{ - 1}}\left( 2 \right)$$