I haven't touched calculus in around a year and a half. However, this semester, I have to take Intro to Electrical Engineering as a requirement for my Computer Engineering major, and the first part of this class seems quite heavy on calculus. One of the problems I've been assigned is as follows:
The voltage and current at the terminals of the circuit element in Fig 1.5 are zero for $t < 0$. For $t \geq0$ they are:
v $= (16,000t + 20)e^{-800t}$ V
i $= (128t + 0.16)e^{-800t}$ A
At what instant of time is maximum power delivered to the element?
Now, I thought that all I had to do was multiply v times i and find the derivative of that equation, then find the maximum based on that, and then find the value of t for that. However, I tried that method on a practice problem and it didn't give me the correct answer. Additionally, the next part of this question is to actually find the maximum value for p, which makes it seem odd that I'd need to find the maximum value first, then the time at which it is at a maximum. So, please, help me figure out the actual method to solving this problem.
EDIT: Also, for clarity, Fig 1.5 simply shows an ideal circuit element, it isn't really necessary for solving the problem.