CAIE IGCSE Additional Math 14.6 Find Stationary Points Questions

Practise solving derivative equations to locate stationary points, determine exact coordinates and analyse how curve features arise from the roots.

Exam points

Set the first derivative to zero to locate stationary points, then solve for their coordinates and interpret the resulting curve behaviour.

[Maximum number: 6]

Show that the curve $y=x-\ln \left(x^{2}+2 x\right)$ has exactly one stationary point.
Find the x-coordinate of this point.

$\frac{dy}{dx}=1-\frac{2x+2}{x^2+2x}$
B1 for $\frac{d(-\ln(x^2+2x))}{dx}=\frac{1}{x^2+2x}\times f(x)$ soi.
Equates their first derivative to 0 and simplifies as far as 2(x+1)=x(x+2) oe
M1 FT their $\frac{dy}{dx}$ .
$x^2-2=0$ or $x^2=2$ $x=\sqrt{2}$ [ $x=-\sqrt{2}$ ]
Justification that the negative solution should be rejected, e.g. $x=-\sqrt{2}$ gives $y=2-\ln(2-2\sqrt{2})$ , which is impossible.

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CAIE IGCSE Additional Math 14.6 Find Stationary Points Questions question 1