Lets consider the problem of designing a railroad track to make a smooth transition between sections of

Question:

Let’s consider the problem of designing a railroad track to make a smooth transition between sections of straight track.
Existing track along the negative x-axis is to be joined smoothly to a track along the line y = 1 for x > 1.
(a) Find a polynomial P = P(x) of degree 5 such that the function F defined by

if x<0 Р<x) if O <х<1 if x> 1 F(x) =