CAIE A-Level Mathematics 1.7.4 Stationary points

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

Exam points

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: 2]

Figure for Question 1.7.4—Stationary points question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve with equation $y=9\left(x^{-\frac{1}{2}}-4 x^{-\frac{3}{2}}\right)$ . The curve crosses the x-axis at the point A.

Find the x-coordinate of the maximum point of the curve.

$9 x^{-\frac{5}{2}}\left(-\frac{1}{2} x+6\right)=0$
M1
Set their $\frac{\mathrm{d} y}{\mathrm{~d} x}$ to zero and an attempt to solve.
x=12
A1
Condone $( \pm) 12$ from use of a correct method.

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1.7.4—Stationary points question 1