Could you check this question to see if I have done it right:
Question: Find the equation of the normal to the curve y=x+ 4/x at the point p where x=4. If the normal meets the curve agian at N, find the co-ordinates of N.
This is what I have done:
dy/dx= 1 - 4x^-2
x=4 y=(4)*4(4)^-1 = 5
dy/dx= 1 - 4(4)^-2 = 0.75 or 3/4
Normal gradient = -4/3
(y - 5) = -4/3(x - 4)
y - 5 = -4/3x + 16/3
y = -4/3x + 31/3 or 3y = - 4x + 31
This is where I got up to, i'm not to sure what you have to do when it says 'If the normal meets the curve agian at N, find the co-ordinates of N'
If you could please explain and check if I have done the first bit right.