suppose y'''=-6 y''(0)=2 y(1)=1 and y(2)=7
what is y ?
if y"'= -6
then
y" = -6 x + c
when x = 0, y"=2 = c
so
y" = -6x + 2
y' = -3 x^2 + 2 x + d
y = -x^3 + x^2 + d x + e
1 = -1 + 1 + d + e
7 = -8 + 4 +2d + e
so
1 d + e = 1
2 d + e = 11
------------------
-d = -10
d = 10 so e = -9
and
y = -x^3 + x^2 + 10 x - 9