Ratio f prime over f

Let $f:\mathbb{R}\to \mathbb{R}$ be defined by $f(x)=(1-x{)}^2\sin (x^2)$ for x ∈ (0, 1) and f(x) = 0 otherwise, and let f′ be its derivative. Let S = {$c\in \mathbb{R}:f^{\prime }(x)\le cf(x)$ for all $x\in \mathbb{R}$}. Which one of the following is true?