The curve C has equation y = f(x), x>0 and f'(x) =4x-6√x+(8/x^2). Given that the point P(4,1) lies on C

a) Find f(x) and simplify your answer

b) Find an equation of the normal to C at the point P (4,1)

For a) I have -4x^(3/2)+2x^2-(8/x)+3 How to simplify this further?

For b) I have 2x+9y-17=0 Is this O.K.?

Thanks in advance.