Classify stationary points

Determine whether a stationary point is a maximum or minimum using the second derivative test or sign changes of the first derivative.

1 questions · Standard +0.3

1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07p Points of inflection: using second derivative
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Pre-U Pre-U 9794/2 Specimen Q9
11 marks Standard +0.3
9 A curve has equation $$y = \mathrm { e } ^ { 3 x } - 5 \mathrm { e } ^ { 2 x } + 8 \mathrm { e } ^ { x }$$
  1. Find the exact coordinates of the stationary points of \(y\).
  2. Determine the range of values of \(x\) for which $$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } > 0$$
  3. Determine the nature of the stationary points on the curve.