How to show that $e^x$ can be approximated by the polynomial $P_{(4)} (x) $to within 0.025 for all values of x on the interval [−1,1]?

Question

How to show that $e^x$ can be approximated by the Taylor polynomial $P_{(4)} (x)$ within $0.025$ on the interval $[−1,1]$?

What is the logic of this question? Should I use Taylor's formula and find a remainder $R$ such $R< 0.025$, and then show that the last term in $P_{(4)} (x)$ which is $\frac{x^4}{4!}$ is greater than $R$?