◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2012 · Q76 Marks

Given that f(x) = x² - 648/√x, find the value of x for which f''(x) = 0.

  1. Given that f(x) = x² - 648/√x, find the value of x for which f''(x) = 0.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [1] Writes 648/√x as 648x^(-1/2) B1
  2. [1] Differentiate (f'(x)) M1
  3. [1] f'(x) = 2x+324x^(-3/2) A1
  4. [1] Differentiate (f''(x)) M1
  5. [1] f''(x) = 2-486x^(-5/2) A1
  6. [1] Solve f''(x) = 0 M1
  7. [1] x = 9 A1

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 and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 2 Variant 1, question 7.

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

Related Additional Mathematics questions

Differentiation and integrationMay/June 20118m

A particle moves in a straight line so that, t s after passing through a fixed point O, its velocity, v ms⁻¹, is give…

Differentiation and integrationMay/June 20127m

Find the equation of the tangent to the curve y = x³ + 2x² – 3x + 4 at the point where the curve crosses the y-axis.

Differentiation and integrationMay/June 20129m

Variables x and y are such that y = e^(2x) + e^(-2x).

Simultaneous equationsMay/June 20107m

The line y = x + 4 intersects the curve 2x² + 3xy − y² + 1 = 0 at the points A and B. Find the length of the line AB.

Equations, inequalities and graphsMay/June 201010m

Given that A = (2 3 / 1 -5) and B = (7 4 / 2 8), calculate 2A,

Vectors in two dimensionsMay/June 20108m

In this question, (1 / 0) is a unit vector due east and (0 / 1) is a unit vector due north. A lighthouse has position…

← Browse all past-paper questions

© 2026 Oracle Prep