A curve has equation \(y=\left(\dfrac{x^2-1}{x^2+1}\right)^4\).
Show that \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) can be written as \(\dfrac{Ax(x^2-1)^3}{(x^2+1)^5}\), where \(A\) is a positive integer to be found.[5]
Show that the curve has stationary points where \(x=-1\), \(x=0\) and \(x=1\).[1]
Use the first derivative test to determine which two stationary points have the same nature and state whether they are maximum or minimum points.[2]