I'm required to show that:

$\displaystyle |e^x - (1+ \frac{x}{1!} + \frac{x^2}{2!})| \leq e/6$

for all $\displaystyle x \in [0,1]$

I'm not sure how to show that the equation is true at the boundries [0,1]. Does anyone know how exactly we can show that $\displaystyle e^x - (1+ \frac{x}{1!} + \frac{x^2}{2!})$ is monotonic in x?

Any help is very much appreciated.