Example 1 (2004 National College Entrance Examination Chongqing Paper) Given the curve $y$ $=\frac{1}{3} x^{3}+\frac{4}{3}$, then the equation of the tangent line passing through point $P(2,4)$ is
It is known that point $P(2,4)$ lies on the curve $y=\frac{1}{3} x^{3}+\frac{4}{3}$, and $k_{P}=\left.y^{\prime}\right|_{x=2}=4$, so the equation of the tangent line is $y-$ $4=4(x-2)$, which simplifies to $4 x-y-4=0$.