Given a standard brownian motion $W_t$ and defining $\tau$ as:
$\tau :=inf\{t\geq0:W_t=1$ or $W_t=-2\}$
The proof below shows that the stopping time is finite:
$P(\tau < t) \geq (|W_t|>2)\\$
$=1-P(|W_t| \leq 2)\\$
$\geq1-4\frac{d}{dt}P(W_t \leq t)|_{t=0}$
$=1-\frac{4}{\sqrt{2 \pi t}}$
$\rightarrow 1$ as $t\rightarrow \infty$
It's all staighforward except the line were the derivative is used:
$\geq1-4\frac{d}{dt}P(W_t \leq t)|_{t=0}$
How does this line relate to the line above?