YLL討論網

Let p(x)=Ax^2 +Bx +D,prove that for any interval[a,b]the value c guaranteed by the mean value theorem is the midpoint of the interval

If  [p（b）-p（a）]/（b-a）=p’(c)
then
[p（b）-p（a）]/（b-a）=A(b+a)+B=p’(c)
then
A(b+a)+B=2Ac+B
therefore
c=(a+b)/2