Calculate the gradient of the chord of the curve \(y = x ^ { 2 } - 2 x\) joining the points at which the values of \(x\) are 5 and 5.1.
Given that \(\mathrm { f } ( x ) = x ^ { 2 } - 2 x\), find and simplify \(\frac { \mathrm { f } ( 5 + h ) - \mathrm { f } ( 5 ) } { h }\).
Use your result in part (ii) to find the gradient of the curve \(y = x ^ { 2 } - 2 x\) at the point where \(x = 5\), showing your reasoning.
Find the equation of the tangent to the curve \(y = x ^ { 2 } - 2 x\) at the point where \(x = 5\).
Find the area of the triangle formed by this tangent and the coordinate axes.