Let $f(x) = \frac{{1 - x}}{{1 + x}}$ and $g(x) = \sqrt {x + 1}$, $x > - 1$.

Find the set of values of $x$ for which $f'(x) \leqslant f(x) \leqslant g(x)$ .

$f'(x) = \frac{{ - 2}}{{{{\left( {1 + x} \right)}^2}}}$     M1A1

Note: Alternatively, award M1A1 for correct sketch of the derivative.

find at least one point of intersection of graphs     (M1)

$y = f(x)$ and $y = f'(x)$ for $x = \sqrt 3$ or $1.73$     (A1)

$y = f(x)$ and $y = g(x)$ for $x = 0$     (A1)

forming inequality $0 \leqslant x \leqslant \sqrt 3$ (or $0 \leqslant x \leqslant 1.73$)     A1A1     N4

Note: Award A1 for correct limits and A1 for correct inequalities.

[7 marks]

Most students were able to find the derived function correctly, although attempts to solve the inequality algebraically were often unsuccessful. This was a question where students prepared in good use of GDC were able to easily obtain good marks.