Let \( f:(0, \infty) \rightarrow(0, \infty) \) be a derivable function and \( F(x) \) is the pri... VIDEO
Let \( f:(0, \infty) \rightarrow(0, \infty) \) be a derivable function and \( F(x) \) is the primitive of \( f(x) \) such that \( 2(F(x)-f(x))=f^{2}(x) \) for any real positive \( x \)
(a) \( f \) is strictly increasing
(b) \( \lim _{x \rightarrow \infty} \frac{f(x)}{x}=1 \)
(c) \( f \) is strictly decreasing
(d) \( f \) is non-monotonic
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