Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The diagram illustrates the curve with equation $y = (\ln x)^2 - 2\ln x$. The curve intersects the $x$-axis at the points $A$ and $B$, and it has a minimum point $M$.
(a)[6]

Find the exact value of the gradient of the curve at each of the points $A$ and $B$.

(b)[2]

Find the exact $x$-coordinate for $M$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Obtain the value $x=1$.

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