4. Given the curve $y=x^{3}-x$, draw a tangent line to the curve from a point $A(t, 0)$ on the $x$-axis, then the maximum number of tangent lines is $\qquad$.
4. 3 Detailed Explanation: Let the point of tangency be $\left(x_{0}, x_{0}^{3}-x_{0}\right)$, then the slope of the tangent line is $k=3 x_{0}^{2}-1$, and the tangent line is $y-\left(x_{0}^{3}-x_{0}\right)=\left(3 x_{0}^{2}-1\right)\left(x-x_{0}\right)$, which simplifies to $y=\left(3 x_{0}^{2}-1\right) x-2 x_{0}^{3}$. Substituting $A(t, 0)$ gives $\left(3 x_{0}^{2}-1\right) t-2 x_{0}^{3}=0$, which is a cubic equation in $x_{0}$ and can have at most three real roots.