It is proved that if f (x) has second derivative on [a, b], f (a) = f (b), and f (x) = (x-a) ^ 2F (x), then there is at least one point ξ ∈ (a, b), f (ξ) = 0

It is proved that if f (x) has second derivative on [a, b], f (a) = f (b), and f (x) = (x-a) ^ 2F (x), then there is at least one point ξ ∈ (a, b), f (ξ) = 0

Right? F (x) = 1, obviously f (x) has second derivative and f (b) = f (a), then f (x) = (x-a) ^ 2, there is no such ξ