The resistance of a device component decreases as the current through it increases and it is described by the relation $R=\frac{0.21}{I-4}$where I is the current. Determine the minimum power delivered. (Assume $I > 4$)

∴ Power of the electric device, P=I²R

$=I^2\cdot \frac{0.2I}{I-4}=\frac{0.2I^3}{I-4}$

Power will be minimum, if $\frac{dP}{dI}=0$

$\begin{array}{l}\frac{d}{dI}\left(\frac{0.2I^3}{I-4}\right)=0\\ \frac{(I-4)\times 0.2\times 3I^2-0.2I^3}{(I-4{)}^2}=0\\ 0.6I^3-2.4I^2-0.2I^3=0\\ 0.4I^3-2.4I^2=0\\ 0.4I^2(I-6)=0(\because I>4)\end{array}$

So, I=6A.

$P_{min}=\frac{0.2\times 6^3}{6-4}=\frac{43.2}{2}=21.6\mathrm{W}$