\( f(x) \) is a twice differentiable function and \( g(x) \) is defined as \( \mathrm{g}(x)=\lef...

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\( f(x) \) is a twice differentiable function and \( g(x) \) is defined as \( \mathrm{g}(x)=\left(f^{\prime}(x)\right)^{2}+f^{\prime \prime}(x) \cdot f(x) \) on \( \left[x_{1}, x_{2}\right] \). If \( x_{1}x_{2}x_{3}x_{4} \) \( x_{5}x_{6}x_{7}, f\left(x_{1}\right)=0, f\left(x_{2}\right)=2, f\left(x_{3}\right)=-3, f\left(x_{4}\right)=4, f\left(x_{5}\right) \) \( =-5, f\left(x_{6}\right)=6 \), and \( f\left(x_{7}\right)=0 \), then the minimum number of real roots of \( g(x)=0 \) can be
(a) 8
(b) 9
(c) 10
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