Tangents to the curve y = x3 at x = –1 and x = 1 are

$y=x^3 \Rightarrow \frac{d y}{d x}=\left.3 x^2 \Rightarrow \frac{d y}{d x}\right|_{x=-1}=3$

and $\left.\frac{d y}{d x}\right|_{x=1}=3$. Hence tangents are parallel.