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 $g(x)=\left(f^{\prime}(x)\right)^2 +f^{\prime \prime}(x) f(x)$ in the interval $[a, e]$ is :