The diagram depicts the curve $y = \frac{\tan^{-1} x}{\sqrt{x}}$ and its maximum point $M$, at which $x = a$.
(a)[4]
Show that $a$ obeys the equation $a = \tan\left(\frac{2a}{1 + a^2}\right)$.
(b)[2]
Verify through calculation that $a$ lies between $1.3$ and $1.5$.
(c)[3]
Use an iterative formula based on the equation in part (a) to find $a$ correct to 2 decimal places. Give each iteration to 4 decimal places.
Worked solution & mark scheme
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