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

$i_2(t)=0,t<mn>0</mn>$

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

Find the power for the inductor:

$p(t)=v(t)i(t)$

$=(-9\mathrm{.}6e^{-300t}+38\mathrm{.}4e^{-1200x})(8e^{-300x}-8e^{-1200t})$

$=-76\mathrm{.}8e^{-600t}+384e^{-1500}-307\mathrm{.}2e^{-2400}W$

To find the max power and the time at which the power is max, take the first derivative of $p(t)$ and set it equal to $0.$