Answer
(a) $Q'(t) = 4.75~A$
(b) $Q'(t) = 5~A$
At time $t = \frac{2}{3}~s$, the current is the lowest.
Work Step by Step
$Q(t) = t^3-2t^2+6t+2$
$Q'(t) = 3t^2-4t+6$
(a) We can find the current at $t=0.5~s$:
$Q'(t) = 3t^2-4t+6$
$Q'(t) = 3(0.5)^2-4(0.5)+6$
$Q'(t) = 4.75~A$
(b) We can find the current at $t=1~s$:
$Q'(t) = 3t^2-4t+6$
$Q'(t) = 3(1)^2-4(1)+6$
$Q'(t) = 5~A$
We can find the time when the current is the lowest:
$Q'(t) = 3t^2-4t+6$
$Q''(t) = 6t-4 = 0$
$t = \frac{2}{3}~s$
At time $t = \frac{2}{3}~s$, the current is the lowest.
