Let be a thrice continuously differentiable function.Prove or disprove that between two consecutive roots of there exist atmost roots of
suppose are two consecutive zeros of suppose has 4 zeros such that then by Rolle's theorem there exist
such that again by Rolle's theorem there exist such that finally, again, by Rolle's theorem there exists such
that but obviously which contradicts our assumption that are two consecutive zeros of so can have at most 3 zeros between