Edexcel C2 — Question 3 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind stationary points
DifficultyModerate -0.3 This is a straightforward stationary point question requiring differentiation (including the power rule for x^{-2}), setting dy/dx = 0, and solving a simple cubic equation. While it involves multiple steps for 6 marks, the techniques are standard C2 material with no conceptual challenges—slightly easier than average due to its routine nature.
Spec1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives
Find the coordinates of the stationary point of the curve with equation $$y = x + \frac{4}{x^2}.$$ [6]
AnswerMarks Guidance
\(\frac{dy}{dx} = 1 - 8x^{-3}\)M1 A1
For SP, \(1 - 8x^{-3} = 0\)M1
\(x^3 = 8\)
\(x = 2\) \(\therefore (2, 3)\)M1 A2 (6) 
$\frac{dy}{dx} = 1 - 8x^{-3}$ | M1 A1 |
For SP, $1 - 8x^{-3} = 0$ | M1 |
$x^3 = 8$ | |
$x = 2$ $\therefore (2, 3)$ | M1 A2 | (6)
Find the coordinates of the stationary point of the curve with equation
$$y = x + \frac{4}{x^2}.$$ [6]

\hfill \mbox{\textit{Edexcel C2  Q3 [6]}}
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Q1 4 Q2 4 Q3 6 Q4 8 Q5 8 Q6 9 Q7 9 Q8 13 Q9 14