Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

The diagram presents a segment of the curve $y = \frac{8}{\sqrt{x}} - x$ together with the points $A(1,7)$ and $B(4,0)$, both of which are on the curve. The tangent to the curve at $B$ meets the line $x = 1$ at $C$.
(i)[4]

Find the coordinates of point $C$.

(ii)[5]

Find the area of the shaded part.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate differentiation of $y=\dfrac{8}{\sqrt{x}}-x$” …

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