Finding the equation of tangent and normal

I have the curve C with equation $\displaystyle 3x^{3/2} - \frac{32}{x} $

First need to find equation of the tangent to C at the point where x = 4, and then the equation of the normal to C at the point where x = 4.

All of the questions on my past exam papers are relatively simple however this one seems to be more challenging.

To tell you my working thus far I differentiated the curve to get $\displaystyle 4.5x^{1/2} + 32x^{-2} $ and rearranged it into the form of

$\displaystyle 4.5x^{1/2} + \frac{32}{x^2} $

And noted that if x was equal to 4, then I would have

$\displaystyle 4.5(4)^{1/2} + \frac{32}{4^2} $ which can be written as 9 + 2, which is 11.

I'm not sure what that information is telling me, let alone if it is correct or not. Could you please help?