12 A function is defined by \(\mathrm { f } ( x ) = x ^ { 3 } - x\).
- By considering \(\frac { f ( x + h ) - f ( x ) } { h }\), show from first principles that \(f ^ { \prime } ( x ) = 3 x ^ { 2 } - 1\).
- Sketch the gradient function \(\mathrm { f } ^ { \prime } ( x )\).
- Show that the curve \(y = f ( x )\) has a single point of inflection which is not a stationary point.