The curve y = e⁻⁴ˣ tan x has two stationary points in the interval 0 < x < ½π.

Mark scheme

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

1. [M1] Use correct product rule or quotient rule, and attempt at chain rule
2. [A1] Obtain correct derivative in any form
3. [M1] Use trigonometric formulae to express derivative in the form ke⁻⁴ˣ sin x cos x sec² x + ae⁻⁴ˣ sec² x or ke⁻⁴ˣ (sin x cos x / (cos x cos x)) + ae⁻⁴ˣ sec²x or sec²x(ke⁻⁴ˣ sin x cos x + ae⁻⁴ˣ)
4. [A1] Obtain correct answer with a = 1 and b = −2
5. [M1] Equate derivative to zero and use correct method to solve for x
6. [A1] Obtain answer, e.g. x = π/12
7. [A1 FT] Obtain second answer, e.g. 5π/12 and no other in the given interval