Let f : ℝ → ℝ be defined by
\(f(x)=\left\{\begin{array}{lr} (1-x)^2 \sin \left(x^2\right), & x \in(0,1) \\ 0, & \text { otherwise } \end{array}\right.\)
and f' be its derivative. Let
S = {c ∈ ℝ : f'(x) ≤ cf(x) for all x ∈ ℝ}.
Which one of the following is true?
1
S = Ø
2
S = Ø and S is a proper subset of (1, ∞)
3
(2, ∞) is a proper subset of
4
S ∩ (0, 1) ≠ Ø