The air inside an airtight syringe is compressed so that its volume, \(V\) cm\(^3\), decreases.
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The air pressure, \(P\) Newtons per cm\(^3\), whithin the syringe is inversely proportional to the volume so that&nbsp;\(PV = 135\). At a given time, the volume of air is \(20\) cm\(^3\) and is decreasing at a rate of \(8\) cm\(^3\) per minute. Find the rate of increase in the air pressure at this time.[4]

The air inside an airtight syringe is compressed so that its volume, \(V\) cm\(^3\), decreases.

The air pressure, \(P\) Newtons per cm\(^3\), whithin the syringe is inversely proportional to the volume so that \(PV = 135\).

At a given time, the volume of air is \(20\) cm\(^3\) and is decreasing at a rate of \(8\) cm\(^3\) per minute.

Find the rate of increase in the air pressure at this time.

Applications of Differentiation

International Baccalaureate Mathematics: Analysis and Approaches Standard Level

2026 MAY TZA P2 Q6

2026 MAY TZA P2 Q6