Find stationary points and nature

A question is this type if and only if it asks to both find the coordinates of stationary points and determine their nature (maximum/minimum).

26 questions · Standard +0.2

1.07n Stationary points: find maxima, minima using derivatives
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AQA C3 2007 June Q7
10 marks Standard +0.3
7
  1. A curve has equation \(y = \left( x ^ { 2 } - 3 \right) \mathrm { e } ^ { x }\).
    1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
    2. Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
    1. Find the \(x\)-coordinate of each of the stationary points of the curve.
    2. Using your answer to part (a)(ii), determine the nature of each of the stationary points.