A particle moves along a line with displacement $x = t^{3} - 6 t^{2} + 9 t$ metres at time $t$ seconds. At what time $t > 0$ is the particle first at rest?

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What is the area enclosed between the curve $y = x^{2}$ and the line $y = x$ ?
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A rectangle has a fixed perimeter of 24 units. What is the greatest possible area of the rectangle?
For events $A$ and $B$ , $P (B) = 0.5$ and $P (A \cap B) = 0.25$ . What is $P (A ∣ B)$ ?