Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is defined by $\frac{d^2y}{dx^2} = -4x$. It reaches a maximum at $(2,12)$.
(i)[6]

Determine the equation of the curve.

(ii)[2]

A point $P$ travels along the curve so that the $x$-coordinate is increasing at $0.05$ units per second. Determine the rate of change of the $y$-coordinate when $x = 3$, and state whether the $y$-coordinate is increasing or decreasing.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: After integrating, obtain $\frac{dy}{dx}=-2x^2+c$

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