Q 1621767621.     If the function `f(x) = {tt(( -x, x < 1),(a + \cos^{-1}(x + b) , 1\le x \le 2))`. is differentiable at `x = 1`, then `\ frac {a}{b}` is equal to:

JEE 2016 Mains 9 April
A

`frac {-\pi - 2}{2}`

B

`frac {\pi + 2}{2}`

C

`frac {\pi - 2}{2}`

D

`-1 -\cos^{-1}(2)`

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