Answer
(a)
$D'(3)$ = $-2.515sin[0.503(3-6.75)]$ $\approx$ $2.39$
(b)
$D'(6)$ = $-2.515sin[0.503(6-6.75)]$ $\approx$ $0.93$
(c)
$D'(9)$ = $-2.515sin[0.503(9-6.75)]$ $\approx$ $-2.28$
(d)
$D'(12)$ = $-2.515sin[0.503(12-6.75)]$ $\approx$ $-1.21$
where the positive derivatives indicate the tide is rising and the negative derivatives indicate the tide is falling.
Work Step by Step
$D(t)$ = $7+5cos[0.503(t-6.75)]$
$D'(t)$ = $-2.515sin[0.503(t-6.75)]$
(a)
$D'(3)$ = $-2.515sin[0.503(3-6.75)]$ $\approx$ $2.39$
(b)
$D'(6)$ = $-2.515sin[0.503(6-6.75)]$ $\approx$ $0.93$
(c)
$D'(9)$ = $-2.515sin[0.503(9-6.75)]$ $\approx$ $-2.28$
(d)
$D'(12)$ = $-2.515sin[0.503(12-6.75)]$ $\approx$ $-1.21$
where the positive derivatives indicate the tide is rising and the negative derivatives indicate the tide is falling.
