Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

A curve is given by $y = (5 - 2x)^{\tfrac{3}{2}} + 5$ for $x < \tfrac{5}{2}$.
(a)[4]

Point $P$ travels along the curve so that its $y$-coordinate is falling at $5$ units per second. Find how fast the $x$-coordinate of point $P$ is rising when $y = 32$.

(b)[6]

The $y$-coordinate of point $A$ on the curve is 32. At point $B$ on the curve, the gradient of the curve is $-3$. Find the equation of the perpendicular bisector of $AB$. Give your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Determines $x=-2$

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