Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is defined by $y = \tfrac{1}{6}(2x-3)^3 - 4x$.
(i)[3]

Calculate $\tfrac{dy}{dx}$.

(ii)[3]

Find the equation of the tangent to the curve at the point where the curve crosses the $y$-axis.

(iii)[3]

Find the set of values of $x$ for which $\tfrac{1}{6}(2x-3)^3 - 4x$ is an increasing function of $x$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $y=\frac16(2x-3)^3-4x$ accurately, apart from the constant term.” …

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