The diagram shows the curve $$\(y=\frac{\tan ^{-1} x}{\sqrt{x}}\)$$ and its maximum point $$\(M\)$$ where $$\(x=a\)$$. Show that $$\(a\)$$ satisfies the equation  $$\( a=\tan \left(\frac{2 a}{1+a^{2}}\right) . \)$$ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Answer:

Knowledge points:

Solution: