Mathematics · Calculus

Let f : R → R be a twice differentiable function such that f''(x) > 0 for all x ∈ R and f'(a - 1) = 0, where a is real number. Let g(x) = f (tan2x - 2tan x + a), 0 < x < π/2. Consider the following two statements: (I) g is increasing in (0, π/4) (II) g is decreasing in (π/4, π/2) Then,