CAIE A-Level Mathematics AS 1.7.4 Stationary Points Questions

Practise applying numerical methods within the AS mathematics syllabus.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 2]

Figure for Question CAIE A-Level Mathematics AS 1.7.4 Stationary Points Questions 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.

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

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CAIE A-Level Mathematics AS 1.7.4 Stationary Points Questions question 1