If x0,x1,x2,y0,y1,y2 are any real numbers prove that there's only one polynomial such that:

f(x0) = yo , f(x2)= y2, f'(x1)= y1

with

x1 > (x0 + x2)/2 .


What happens if x1 = (x0 + x2)/2 ?

Thanks in advance