2 The curve with equation \(y = x ^ { 4 } - 32 x + 5\) has a single stationary point, \(M\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Hence find the \(x\)-coordinate of \(M\).
- Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
- Hence, or otherwise, determine whether \(M\) is a maximum or a minimum point.
- Determine whether the curve is increasing or decreasing at the point on the curve where \(x = 0\).