On a particular day, the power used in a particular state $($in thousands of megawatts$)$ could be approximated by the function $P(t)=-0\mathrm{.}005449t^3+0\mathrm{.}1886t^2-0\mathrm{.}6963t+20\mathrm{.}05,$ where $t$ is the number of hours since midnight, for $0t24.$ Find any relative extrema for power usage, as well as when they occurred.

Find the derivative of $P(t).$

$P^{\text{'}}(t)=-0\mathrm{.}016347t^2+0\mathrm{.}3772t-0\mathrm{.}6963$

Find any relative extrema for power usage, as well as when they occurred. First find the relative minima. Select the correct choice below and, if necessary, fill in any answer boxes within your choice.

A$.$ There are no relative minima for power usage.

B$.$ There are two relative minima for power usage. The relative minimum power usage that occurs first is thousand megawatts and it occurs hours after midnight. The relative minimum power usage that occurs second is thousand megawatts and it occurs hours after midnight.

$($Do not round until the final answer. Then round to ty$/$o decimal places as needed.$)$

C$.$ There is one relative minimum for power usage. The relative minimum power usage is thousand megawatts and it occurs hours after midnight.

$($Do not round until the final answer. Then round to two decimal places as needed.$)$

Find the relative maxima. Select the correct choice below and, if necessary, fill in any answer boxes within your choice.

A$.$ There are no relative maxima for power usage.

B$.$ There are two relative maxima for power usage. The relative maximum power usage that occurs first is thousand megawatts and it occurs hours after midnight. The relative maximum power usage that occurs second is thousand megawatts and it occurs hours after midnight.

$($Do not round until the final answer. Then round to two decimal places as needed.$)$

C$.$ There is one relative maximum for power usage. The relative maximum power usage is thousand megawatts and it occurs hours after midnight.

$($Do not round until the final answer. Then round to two decimal places as needed.$)$