12.6.7 Higher Mathematics

Condition: function \ (f \) twice continuously differentiated on the segment \ ([a, b] \) and we have at this segment of at least three different zeros. Prove that there is a point \ (x \ in [a, b] \) such that equality \ (f (x)+f^{\ prime \ prime} (x) = 2 f {\ prime} (x) \) is performed