Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve satisfies $\frac{dy}{dx} = \frac{3}{(1 + 2x)^2}$, and the point $(1, \frac{1}{2})$ lies on it.

(i)[4]

Find the equation satisfied by the curve.

(ii)[3]

Find all values of $x$ for which the gradient of the curve is less than $\frac{1}{3}$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly integrates to $y=\frac{3}{-2(1+2x)}+c$” …