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Let \( g(x)=\int_{0}^{x}\left(3 t^{2}+2 t+9\right) d t \) and \( f(x) \) be a decreasing
P
W function, \( \forall x \geq 0 \) such that \( \mathbf{A B}=f(x) \hat{\mathbf{i}}+g(x) \hat{\mathbf{j}} \) and \( \mathrm{AC}=g(x) \hat{\mathbf{i}}+f(x) \hat{\mathbf{j}} \) are the two smallest sides of a \( \triangle A B C \) Which of the following is true (for \( x0 \) )?
(a) \( f(x)0, g(x)0 \)
(b) \( f(x)0, g(x)0 \)
(c) \( f(x)0, g(x)0 \)
(d) \( f(x)0, g(x)0 \)
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