The function `f(x) = x^3 - 6x^2 + ax + b` is such that `f(2) = f(4) = 0`. Consider two statements.
(S1) there exists `x_1, x_2 in (2,4), x_1 lt x_2`, such that `f' (x_1) = - 1 and f'(x_2) = 0`.
(S2) there exists `x_3, x_4 in (2, 4), x_3 lt x_4`, such that f is decreasing in `(2 , x_4)`, increasing in `(x_4,4) and 2f'(x_3) = sqrt3 f(x_4)`.

Options

A. (S1 ) is false and (S2) is true
B. both (S1 ) and (S2) are true
C. (S1 ) is true and (S2) is false
D. both (S1 ) and (S2) are false