18M.1.AHL.TZ2.H_4

pestleMathematicsAIHLPaper 118M· sl-5-6-stationary-points-local-max-and-minsource ↗

Consider the curve $y = \frac{1}{{1 - x}} + \frac{4}{{x - 4}}$ .

Find the x-coordinates of the points on the curve where the gradient is zero.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid attempt to find $\frac{{{\text{d}}y}}{{{\text{d}}x}}$ M1

$\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{{{{\left( {1 - x} \right)}^2}}} - \frac{4}{{{{\left( {x - 4} \right)}^2}}}$ A1A1

attempt to solve $\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0$ M1

$x = 2,\,\,x = - 2$ A1A1

[6 marks]

Examiners’ report

[N/A]