The question states:

The charge entering a certain circuit element is found to be q=5t*e^((-10^3)*t) C. (a) Find the corresponding current i. (b) Find the instant t [greater than or equal to] 0 at which i is minimum, as well as Imin.


For part (a) I just took the derivative and got I=(5-5000*t)*e^(-1000t)



The answer for part b is 2ms, -0.677 A

I plugged those numbers in and got the same result, but I'm just wondering how they figured out it was 2 ms

Thanks!

 

Try finding the derivative of the current. In the point where it is zero, it will have either a maximum or a minimum. Since you know you are looking for a minimum, you can stop there.

If you want to be more specific, you can try to find the value ofsecond derivative of the current on the same point. If it is positive, you have a minimum. If it is negative, you have a maximum.