Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The points $A(2, 9)$ and $B(3, 0)$ are on the curve $y = 9 + 6x - 3x^2$, as the diagram shows. The tangent at $A$ meets the $x$-axis at $C$.

(i)[4]

Find the equation of tangent $AC$ and hence determine the $x$-coordinate of $C$.

(ii)[5]

Find the area of shaded region $ABC$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate derivative $\dfrac{dy}{dx}=6-6x$” …