Mathematics

Problem

Let

f(x)

be a cubic polynomial on

R

which increases in the interval

(-\infty, 0) \cup (1, \infty)

and decreases in the interval

(0, 1)

. If

f'(2) = 6

and

f(2) = 2

then the value of

\tan^{-1}(f(1)) + \tan^{-1}(f(\frac{3}{2})) + \tan^{-1}(f(0))

equals (a)

\tan^{-1}2

(b)

\cot^{-1}2

(c)

-\tan^{-1}2

(d)

-\cot^{-1}2