12.6.7 Higher mathematics

condition: The function \( f \) is twice continuously differentiable on the interval \( [a, b] \) and we have at least three distinct zeros on this interval. Prove that there is a point \( x \in[a, b] \) such that the equality \( f(x)+f^{\prime \prime}(x)=2 f^{\prime}(x) \)