Differentiation - Connected Rates of Change
Differentiation - Connected Rates of Change
When the height of the liquid in a container is \(h\) meters, the volume of liquid is \(V\) m\(^3\), where \(V=0.05[(3h+2)^3-8]\).
- Find an expression for \(\frac{\mathrm{d}V}{dh}\).
- The liquid enters the container at a constant rate of \(0.081\) m\(^3\)/s. Find the rate at which the height of the liquid is increasing when \(V=0.95\) m\(^3\).
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Answer:(a) \(\frac{\mathrm dV}{\mathrm dh}=0.45(3h+2)^2\) (b) \(\frac{\mathrm dh}{\mathrm dt}=\frac{1}{50}\text{ m s}^{-1}\)
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