Example $-$ Assessment Problem $6\mathrm{.}1,$ continued

$i_g(t)=8e^{-300t}-8e^{-1200t}A,t0.$

Find the energy for the inductor:

$w(t)=\frac{1}{2}Li(t{)}^2$

$=\frac{1}{2}(0\mathrm{.}004)(8e^{-300t}-8e^{-120x}{)}^2$

$=128(e^{-600x}-2e^{-150x}+e^{-2400x})mJ$

To find the max energy and the time at which the energy is max, take the first derivative of $w(t)$ and set it equal to o$.$ Or if you don't have w$($t$)$ yet, do the same for $i(t)!$