CAIE A-Level Mathematics 1.7.4 Stationary points

Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise locating stationary points by setting dy/dx=0 and classifying their nature using d²y/dx² or equivalent reasoning.

How this is tested

set dy/dx=0 and solve the resulting equation for stationary coordinates
substitute into d²y/dx² to decide whether a point is a maximum or minimum
use stationary point information to find constants or exact values in curve models

[Maximum number: 7]

The equation of a curve is $y=\frac{8}{3 x-8}-\frac{6}{x-1}$ .

(a)

（b）（i）Find the x－coordinates of each of the stationary points of the curve．

[ 3 ]

(b)

（ii）Find $\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}$ and hence determine the nature of each of the stationary points．

[ 4 ]