Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

For $x > 0$, the function $f$ satisfies $f'(x) = 2x - \frac{2}{x^2}$. Its graph, $y = f(x)$, goes through the point $P(2, 6)$.

(i)[3]

Find the equation for the normal to the curve at $P$.

(ii)[4]

Find the equation for the curve.

(iii)[4]

Find the $x$-coordinate of the stationary point and, with a reason, state whether it is a maximum or a minimum.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate and obtain $f'(2)=\dfrac{7}{2}$” …