The diagram depicts the curve $y = \sqrt{\frac{1 - x}{1 + x}}$.
(i)[5]
Differentiate $\frac{1 - x}{1 + x}$ first to find $\frac{dy}{dx}$ in terms of $x$. Hence prove that the gradient of the normal to the curve at the point $(x, y)$ is $(1 + x)\sqrt{1 - x^2}$.
(ii)[4]
The normal gradient attains its largest value at the point $P$ marked on the diagram. Using differentiation, determine the $x$-coordinate of $P$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $(1-x)/(1+x)$ by applying either the quotient rule or the product rule” …