◈ Oracle PrepSign Up Free
A-LevelMathematicsDifferentiation9709/22 · May/June 2019 · Q35 Marks

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. [DM1] Equate first derivative to zero and attempt value of x from ln x = k oe
  4. [A1] Obtain x = e
  5. [A1] Obtain y = 3e

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2019 Paper 2 Variant 2, question 3.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Mathematics questions

DifferentiationFeb/Mar 20187m

The parametric equations of a curve are x = 2t + sin 2t, y = 1 – 2 cos 2t, for −½π < t < ½π.

DifferentiationFeb/Mar 201811m

A particle P moves in a straight line. The velocity v m s¯¹ at time t s is given by v = 4 + 0.2t for 0 ≤ t ≤ 10, v = …

DifferentiationFeb/Mar 20197m

A curve has equation y = (2x – 1)⁻¹ + 2x.

VectorsFeb/Mar 202210m

The points A and B have position vectors 2i + j + k and i – 2j + 2k respectively. The line l has vector equation r = …

MechanicsFeb/Mar 20224m

A crane is used to raise a block of mass 600kg vertically upwards at a constant speed through a height of 15 m. There…

MechanicsFeb/Mar 20225m

A particle P is projected vertically upwards from horizontal ground with speed ums¯¹. P reaches a maximum height of 2…

← Browse all past-paper questions

© 2026 Oracle Prep