詳解：\(y' = 2x\sqrt {x + 1}  + \frac{{{x^2}}}{{2\sqrt {x + 1} }}\)

\(m = 2 \cdot 3\sqrt 4  + \frac{9}{{2\sqrt 4 }} = 12 + \frac{9}{4} = \frac{{57}}{4}\)

利用點斜式得切線方程式

\(y - 9 = \frac{{57}}{4}\left( {x - 3} \right)\)