6 Given that \(y = 6 x ^ { 3 } + \frac { 4 } { \sqrt { x } } + 5 x\), find
- \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
- \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
\(7 \quad A\) is the point \(( 5,7 )\) and \(B\) is the point \(( - 1 , - 5 )\). - Find the coordinates of the mid-point of the line segment \(A B\).
- Find an equation of the line through \(A\) that is perpendicular to the line segment \(A B\), giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers.