Application Of Derivatives

If \(f(x)\) is a twice differentiable function such that \(f(A)=0, f(B)=2, f(C)=-1, f(D)=2\), \(f(e)=0\), where \(a < b < c < d < e\), then the minimum number of zeroes of \(g(x)=\left(f'(x)\right)^{2}+f''(x) f(x)\) in the interval \([a, e]\) is :