6
\includegraphics[max width=\textwidth, alt={}, center]{918d83c3-1608-4482-9d3d-8af05e65f353-2_394_846_1868_648} The diagram shows part of the curve \(y = x ^ { 2 } + 5\). The point \(A\) has coordinates ( 1,6 ). The point \(B\) has coordinates ( \(a , a ^ { 2 } + 5\) ), where \(a\) is a constant greater than 1 . The point \(C\) is on the curve between \(A\) and \(B\).

1. Find by differentiation the value of the gradient of the curve at the point \(A\).
2. The line segment joining the points \(A\) and \(B\) has gradient 2.3. Find the value of \(a\).
3. State a possible value for the gradient of the line segment joining the points \(A\) and \(C\).