Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram illustrates the curve $y=4x^2-x^3$ together with the tangent drawn at point $P$. The $x$-coordinate of $P$ is $3$.

(a)[5]

Find the equation of the tangent at point $P$. Give your answer in the form $y=mx+c$.

(b)[6]

Find the exact area of the shaded part.

(c(i))[1]

Find the equation of the transformed curve in the form $y = mx^2 + nx^3$, where the integers $m$ and $n$ are to be found.

(c(ii))[2]

State the coordinates of $Q$ and the area of the transformed shaded area.

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\dfrac{dy}{dx}=8x-3x^2$” …