(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The expression for the charge entering an upper terminal of a component is:

q = 1/[itex]\alpha^{2}[/itex] - (t/[itex]\alpha[/itex] + 1/[itex]\alpha^{2}[/itex])e[itex]^{-t\alpha}[/itex]

Find the maximum value of the current entering the terminal if [itex]\alpha[/itex] = 0.03679 s[itex]^{-1}[/itex]

2. Relevant equations

3. The attempt at a solution

Since they gave us the equation for the charge, to find current we simply take the derivative with respect to time of the given equation. I did this and ended up with te[itex]^{-t\alpha}[/itex]. This seems to check out just fine. I then realized that they want the maximum value that this derivative can be. So then I went ahead and took the second derivative and tried to set it equal to 0 (since that would be a local max or min). This ended up being very messy and it didn't work out. Is there an easier way to find the maximum current?

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# Finding Maximum Current Entering A Terminal

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