A curve has equation y = e^(-2x) sin x. (a) Show that dy/dx = e^(-2x) (cos x - 2sin x). (b) Find the x-coordinates of the stationary points of the curve for 0 ≤ x < π. Give your answers to 3 significant figures.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. M1: Uses the product rule to differentiate y = e^(-2x) sin x. (e.g. dy/dx = -2e^(-2x) sin x + e^(-2x) cos x)
2. A1: Correctly differentiated expression.
3. A1: Factors out e^(-2x) to show the given result dy/dx = e^(-2x) (cos x - 2sin x).
4. M1: Sets dy/dx = 0 (or cos x - 2sin x = 0) to find stationary points.
5. A1: Correctly manipulates to tan x = 1/2.
6. A1: Finds the principal value of x = arctan(1/2) = 0.4636... (allow 0.464).
7. A1: No other solutions in the range, so 0.464 (3 s.f.) is the only answer. (Candidates must demonstrate awareness of the domain)