Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

A curve has a stationary point at $(3, 9\tfrac{1}{2})$ and its equation is such that $\frac{dy}{dx} = ax^2 + a^2x$, where $a$ is a non-zero constant.
(i)[2]

Find the value of $a$ from the information given.

(ii)[4]

Find the equation of the curve.

(iii)[2]

Determine, with all necessary working shown, the nature of the stationary point.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $x=3$ into $\frac{dy}{dx}=0$ to obtain $9a+3a^2=0$” …

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