A curve has equation y = (9e^(2x) + 16) / (e^x - 1).

Mark scheme

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

1. [1] Use quotient rule (or equivalent) to find first derivative *M1 Condone poor use of brackets if recovered later
2. [1] Obtain 18e^(2x)(e^x – 1) – e^x(9e^(2x) +16) / (e^x - 1)² OE
3. [1] Equate first derivative to zero and attempt factorisation DM1 Need to be working with 9e^(3x) −18e^(2x) − 16e^x = 0
4. [1] Obtain e^x(3e^x – 8)(3e^x + 2) = 0 AG – necessary detail needed SC B3 If numerator is in incorrect order and given result is obtained. SC B3 If denominator is not squared and given result is obtained.
5. [1] Observe, using given result from part (a), at some stage, e^x ≠0 and 3e^x +2≠0 and hence one stationary point
6. [1] Attempt exact solution for x and for y
7. [1] Obtain x = ln(8/3) or exact equivalent
8. [1] Obtain y = 48 Not from a rounded decimal