3 The curve with equation \(y = x ^ { 5 } + 20 x ^ { 2 } - 8\) passes through the point \(P\), where \(x = - 2\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Verify that the point \(P\) is a stationary point of the curve.
- Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at the point \(P\).
- Hence, or otherwise, determine whether \(P\) is a maximum point or a minimum point.
- Find an equation of the tangent to the curve at the point where \(x = 1\).