The curve with equation y = (2 – sin x) / cos x has one stationary point in the interval -π/2 < x < π/2.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

1. [1] Use correct product or quotient rule or rewrite as 2sec x – tan x and differentiate
2. [1] Obtain correct derivative in any form
3. [1] Equate the derivative to zero and solve for x
4. [1] Obtain x = π/6
5. [1] Obtain y = √3
6. [1] Carry out an appropriate method for determining the nature of a stationary point
7. [1] Show the point is a minimum point with no errors seen