I could really use some help with the following...Any guidance or hints are appreciated.

Let $\displaystyle f(x) := e^x.$

Show that the nth Taylor polynomial for $\displaystyle f$ at 0 is

$\displaystyle T_nf(x) =\sum_{k=0}^{n}\frac{x^k}{k!}$

and the Lagrange Remainder is

$\displaystyle R_nf(x) = e^c\frac{x^{n+1}}{(n + 1)!}$ for some c between 0 and x.