Find the exact coordinates of the stationary point of the curve with equation y = 3x / ln x.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [*M1] Use quotient rule to find first derivative or equivalent
2. [A1] Obtain dy/dx = (3lnx - 3x(1/x)) / (lnx)² or equivalent
3. (Guidance: Condone lack of brackets in denominator unless specifically simplified to 2ln x)
4. [DM1] Equate first derivative to zero and attempt value of x from ln x = k oe
5. (Guidance: Must get as far as x =)
6. [A1] Obtain x = e
7. (Guidance: Allow e¹)
8. [A1] Obtain y = 3e
9. (Guidance: Allow 3 e¹)
10. (Guidance: SC1: If 3lnx - 3x(1/x) = 0 seen with no reference to dy/dx, then allow M1 A1 then following marks)
11. (Guidance: SC2: If denominator incorrect and numerator correct/reversed/added then max marks M0A0M1A1A1)
12. (Guidance: SC3: If numerator reversed then max marks M1A0M1A1A1)