Mathematics 0580 · IGCSE · Differentiation

Differentiation — practice question

The diagram displays the graph of $y = 3x - x^3$. It meets the $x$-axis at $A$, $O$ and $B$, and its turning points are $P$ and $Q$.
(a)[3]

Find the $x$-coordinate of $A$ and the $x$-coordinate of $B$, and give each answer as an exact value.

(b(i))[2]

Differentiate the expression $3x - x^3$.

(b(ii))[4]

Find the coordinates of $P$ and $Q$ from the graph.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: So, $A=-\sqrt{3}$

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