3. Applications of differentiation
Interactive practice questions
The electrical resistance, $R$R, of a component at temperature, $t$t, is given by $R=9+\frac{t}{17}+\frac{t^2}{108}$R=9+t17+t2108.
Find $\frac{dR}{dt}$dRdt, the instantaneous rate of increase of resistance with respect to temperature.
Easy
2min
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=−4x6−5x5+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+1.4t−0.02t2.
Easy
6min
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