Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve satisfies $\frac{dy}{dx} = \frac{6}{(3x - 2)^3}$, and $A\,(1,-3)$ is on it. A point moves along the curve, and at $A$ the $y$-coordinate of the point is rising at $3$ units per second.
(a)[3]

Find the rate at which the $x$-coordinate is increasing at $A$.

(b)[4]

Find the equation for the curve.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “When $x=1$, $\frac{dy}{dx} = 6$” …

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