The diagram shows part of the curve $y=3x^2$. The points $P$ and $Q$ lie on the curve, and hav

Question

The diagram shows part of the curve $y=3x^2$. The points $P$ and $Q$ lie on the curve, and have the same $y$-coordinates. Show that the area of the triangle $OPQ$, $A$ cm$^2$, is given by $A=3x^3$.[2] The points $P$ and $Q$ move along the curve such that their $y$-coordinates are changing at a rate of 3 units per second. Find, at the point where $x=4$, the rate of change of $PQ$,[4] the rate of change of $A$.[3]

Accepted Answer

(a) $A=3x^3\text{ cm}^2$ (b) $\frac{1}{4}\text{ units s}^{-1}$ (c) $18\text{ units}^2\text{ s}^{-1}$

2025 DSS PRELIMS P2 Q9

2025 DSS PRELIMS P2 Q9

Solution:

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