- A curve has the equation \(y = \frac { x } { 2 } + 3 - \frac { 1 } { x } , x \neq 0\).
The point \(A\) on the curve has \(x\)-coordinate 2 .
- Find the gradient of the curve at \(A\).
- Show that the tangent to the curve at \(A\) has equation
$$3 x - 4 y + 8 = 0$$
The tangent to the curve at the point \(B\) is parallel to the tangent at \(A\).
- Find the coordinates of \(B\).