Prove that $\displaystyle e^x \geqslant x+1$

using the taylor series for all $\displaystyle x > 0 $ i can use the taylor series for $\displaystyle e^x$ its obvious that the inequality is true for positive values.

then using the fact that $\displaystyle e^x > 0 $ works for all x less than -1.

but i am jut a bit stuck on proving the inequality for values of x $\displaystyle -1 \leqslant x \leqslant 0 $