SCalcET$93\mathrm{.}7\mathrm{.}024.$EP$.$

Some of the ghest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about $2\mathrm{.}0$ m and at high tide it is about $12\mathrm{.}0$ m $.$ The natural period of oscillation is a little more than $12$ hours, and on a day in June, high tide occurs at $6$:$45a.m.$ This helps explain the following model for the water depth $D($in meters$)$ as a function of the time $t($In hours after midnight$)$ on that day.

$D(t)=75cos[0\mathrm{.}503(t-6\mathrm{.}75)]$

Find the derivative $D^{\text{'}}(t).$

$D^{\text{'}}(t)=$

How fast $($in $\frac{m}{h})$ was the tide rising $($or falling$)$ at the following times? $($Round your answers to two decimal places.$)$

$($a$)2$:$00$ a$.$m$.$

$$ m$/$h

$($b$)3$:$00$ a$.$m$.$

$\frac{m}{h}$

$($c$)10$:$00$ a$.$m$,$

$$ m$/$h

$($d$)$ Noon

$$ m$/$h