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3.01 Rates of change

Interactive practice questions

The volume of gas, $V$V, is related to the pressure, $P$P, by the equation $PV=k$PV=k, where $k$k is a constant.

Find $\frac{dV}{dP}$dVdP, the rate of increase of volume with respect to pressure.

Easy
2min

The asset value of a corporation is expected to change according to the formula $V=-4x^6-5x^5+250x^4+40000$V=4x65x5+250x4+40000.

Easy
2min

The temperature, $T$T, in degrees Celsius of a body at time $t$t minutes is modelled by $T=37+1.4t-0.02t^2$T=37+1.4t0.02t2.

Easy
6min

A company's market research department find that the revenue produced by pricing an item at $p$p dollars is related by the equation $R=-3p^2+45p$R=3p2+45p.

Easy
1min
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Outcomes

3.2.1.2

recognise that 𝑒 is the unique number 𝑎 for which the limit (in 3.2.1.1) is 1

3.2.1.5

identify contexts suitable for mathematical modelling by exponential functions and their derivatives and use the model to solve practical problems; verify and evaluate the usefulness of the model using qualitative statements and quantitative analysis

3.2.3.3

use trigonometric functions and their derivatives to solve practical problems; including trigonometric functions of the form 𝑦 = sin(𝑓(𝑥)) and 𝑦 = cos(𝑓(𝑥)).

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