3 A curve has equation \(y = 2 x ^ { 5 } + 5 x ^ { 4 } - 1\).
- Find:
- \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
- \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\)
- The point on the curve where \(x = - 1\) is \(P\).
- Determine whether \(y\) is increasing or decreasing at \(P\), giving a reason for your answer.
- Find an equation of the tangent to the curve at \(P\).
- The point \(Q ( - 2,15 )\) also lies on the curve. Verify that \(Q\) is a maximum point of the curve.
[0pt]
[4 marks]