You have to show that $\displaystyle f^{(k)}(0)=0$, for all $\displaystyle k\in \mathbb{N}$, so that the Maclaurin series is identical to 0, for all $\displaystyle x\in\mathbb{R}$, but $\displaystyle f(x)\neq 0$, for all $\displaystyle x\in \mathbb{R}\backslash\{0\}$.