Answer
(a) $Q'(0.5)$ = $4.75$ $A$
(b) $Q'(1)$ = $5$ $A$
The current is lowest when $Q'$ has a minimum.
$Q''(t)$ = $6t − 4$ $\lt$ 0 when $t$ $\lt$ $\frac{2}{3}$
So the current decreases when $t$ $\lt$ $\frac{2}{3}$
and increases when $t$ $\gt$ $\frac{2}{3}$
Thus, the current is lowest at $t$ = $\frac{2}{3}$ s.
Work Step by Step
The quantity of charge is
$Q(t)$ = $t^{3}-2t^{2}+6t+2$
current is
$Q'(t)$ = $3t^{2}-4t+6$
(a) $Q'(0.5)$ = $3(0.5)^{2}-4(0.5)+6$ = $4.75$ $A$
(b) $Q'(1)$ = $3(1)^{2}-4(1)+6$ = $5$ $A$
The current is lowest when $Q'$ has a minimum.
$Q''(t)$ = $6t − 4$ $\lt$ 0 when $t$ $\lt$ $\frac{2}{3}$
So the current decreases when $t$ $\lt$ $\frac{2}{3}$
and increases when $t$ $\gt$ $\frac{2}{3}$
Thus, the current is lowest at $t$ = $\frac{2}{3}$ s.
