Find stationary points of exponential curves

A question is this type if and only if it requires finding and classifying stationary points (maxima/minima) of functions involving exponential terms.

1 questions · Moderate -0.3

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CAIE P3 2002 November Q4
6 marks Moderate -0.3
4 The curve \(y = \mathrm { e } ^ { x } + 4 \mathrm { e } ^ { - 2 x }\) has one stationary point.
  1. Find the \(x\)-coordinate of this point.
  2. Determine whether the stationary point is a maximum or a minimum point.