- The curve \(C\) has equation
$$y = 5 x ^ { 4 } - 24 x ^ { 3 } + 42 x ^ { 2 } - 32 x + 11 \quad x \in \mathbb { R }$$
- Find
- \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
- \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\)
- Verify that \(C\) has a stationary point at \(x = 1\)
- Show that this stationary point is a point of inflection, giving reasons for your answer.