Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The diagram shows the curve whose equation is $y = 2x^2 - \frac{5}{x} + 3$. The curve intersects the $x$-axis at $P(1, 0)$, and $M$ is a minimum point.
(a)[2]

Find the gradient at $P$ on the curve.

(b)[3]

Find the coordinates of $M$. Give both coordinates correct to 3 significant figures.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate so that $4x+\frac{5}{x^2}$ is obtained” …

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