The equation of a curve is y = sin x sin 2x. The curve has a stationary point in the interval 0 < x < ½π. Find the x-coordinate of this point, giving your answer correct to 3 significant figures.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [*M1] Use correct product rule on given expression
2. [A1] Obtain correct derivative in any form
3. [*M1] Use correct double angle formulae to express derivative in terms of sinx and cosx
4. [DM1] Equate derivative to zero and obtain an equation in one trig variable
5. [A1] Obtain 3sin²x = 2, 3cos²x = 1 or tan²x = 2
6. [A1] Solve and obtain x = 0.955
7. [*M1] (Alternative method for first three marks) Use correct double angle formula to obtain y = 2cosx - 2 cos³ x or y = 2sin²x cos x
8. [*M1] (Alternative method for first three marks) Use chain rule and / or product rule
9. [A1] (Alternative method for first three marks) Obtain derivative y' = -2sinx + 6sinxcos²x or y' = -2sin³x + 4sinxcos²x
10. [*M1] (Alternative method for second and third M marks) Equate derivative to zero and obtain an equation in tanx and tan2x
11. [DM1] (Alternative method for second and third M marks) Use correct double angle formula to obtain an equation in tanx