Let f: R → R be a thrice differentiable function such that f(0)=0, f(1)=1, f(2)=-1, f(3)=2 and f(4)=-2. Then, the minimum number of zeros of (3 f^′…

Let $\displaystyle f: \mathbb{R} \rightarrow \mathbb{R}$ be a thrice differentiable function such that $\displaystyle f(0)=0, f(1)=1, f(2)=-1, f(3)=2$ and $\displaystyle f(4)=-2$. Then, the minimum number of zeros of $\displaystyle \left(3 f^{\prime} f^{\prime \prime}+f f^{\prime \prime \prime}\right)(x)$ is $\displaystyle \_\_\_\_$