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f(x) is a twice differentiable function ...

`f(x)` is a twice differentiable function and g(x) is defined as `g(x)=(fprime(x))^2+f prime prime(x)*f(x)` on `[x_1,x_2].` If `x_1 < x_2 < x_3 < x_4 < x_5 < x_6 < x_7,f(x_1)=0,f(x_2)=2,f(x_3)=-3,f(x_4)=4,f(x_5)=-5,f(x_6) and f(x_7)=0,` then the minimum number of real roots of `g(x)=0` can be

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