Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is specified for $x > 0$ and satisfies $\frac{dy}{dx} = x + \frac{4}{x^2}$. The point $P(4, 8)$ lies on it.
(i)[4]

Determine the equation of the curve.

(ii)[4]

Show that the gradient of the curve reaches a minimum when $x = 2$ and state that minimum value.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrates to obtain $y=\frac{x^2}{2}-\frac{4}{x}+c$” …

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