12 A curve, \(C _ { 1 }\) has equation \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x ) = \frac { 5 x ^ { 2 } - 12 x + 12 } { x ^ { 2 } + 4 x - 4 }\)
The line \(y = k\) intersects the curve, \(C _ { 1 }\)
12
- Show that \(( k + 3 ) ( k - 1 ) \geq 0\)
[0pt]
[5 marks]
12
- (ii) Hence find the coordinates of the stationary point of \(C _ { 1 }\) that is a maximum point.
[0pt]
[4 marks]
12 - Show that the curve \(C _ { 2 }\) whose equation is \(y = \frac { 1 } { \mathrm { f } ( x ) }\), has no vertical asymptotes.
[0pt]
[2 marks]
12 - State the equation of the line that is a tangent to both \(C _ { 1 }\) and \(C _ { 2 }\).
[0pt]
[1 mark]