test pbm

COMPREHENTION:
if f:R---->R & f(x) is differentiable function such that all its succesive derivatives exists f'(x) can be taken 0at discrete points only & f(x).f''(x)≤ 0 for all x εR ans following Q now Q1 if α,β are the 2 consecutive roots of f(x)=0 ,then prove f^'''(x)=0.

if f(a)=0,
then prove f(a+h)f^''(a-h)>0