Applications of Exponential & Log Function Derivatives
4. The current in a circuit is given by:
i = 4t2e8/t
Find the times when the current is a minimum or maximum.
We need to take the derivative of i with respect to time, set it equal to zero, and solve.
Use the Product Rule:
di/dt =4t2e8/t (-8/t2) + 8te8/t
0 = e8/t[-32 + 8t]
0 = -32 + 8t
t = 4 sec This is a minimum.