Find the gradient of the curve \(y = 2 x ^ { 2 }\) at the point where \(x = 3\).
At a point \(A\) on the curve \(y = 2 x ^ { 2 }\), the gradient of the normal is \(\frac { 1 } { 8 }\). Find the coordinates of \(A\).
Points \(P _ { 1 } \left( 1 , y _ { 1 } \right) , P _ { 2 } \left( 1.01 , y _ { 2 } \right)\) and \(P _ { 3 } \left( 1.1 , y _ { 3 } \right)\) lie on the curve \(y = k x ^ { 2 }\). The gradient of the chord \(P _ { 1 } P _ { 3 }\) is 6.3 and the gradient of the chord \(P _ { 1 } P _ { 2 }\) is 6.03.
What do these results suggest about the gradient of the tangent to the curve \(y = k x ^ { 2 }\) at \(P _ { 1 }\) ?