Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

For the curve, $\frac{d^2 y}{dx^2} = -\frac{24}{x^3}$. It is also stated that the curve has a stationary point at $(-2, 19)$.
(a)[3]

Determine an expression for $\frac{dy}{dx}$.

(b)[2]

Determine the $x$-coordinate of the curve's other stationary point, and state what kind of stationary point it is.

(c)[3]

Determine the equation of the curve.

(d)[4]

Determine the equation of the normal to the curve at the point where $\frac{dy}{dx} = -\frac{9}{4}$ and $x$ is positive. Give your answer in the form $px + qy + r = 0$, where $p$, $q$ and $r$ are integers.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Derives $\frac{dy}{dx}=\frac{12}{x^2}+c$

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