Sir,
Is Rolle's theorem applicable to all polynomial functions?
Not necessarily. For, eg, the linear functions are not satisfied by rolle's theoram since they are monotonic.
Any non monotonic function will satisfy Rolle's theoram for atleast one value of a in R.
However, if the 3 conditions of Rolle's theoram are satiasfied for any interval [a,b] in R, them Rolle's theoram MUST be satisfied.
what is rolles theorem?
Yes, of course. As all the polynomial functions satisfy three coditions.
Even if a linear function satisfies all three conditons specially f(a) = f(b) then there exists at least on value c ( infinite values in this case) such that
f' (c) =0