The depth ( D metres) of water in a harbour at a time ( t hours)after midnight on a particular day can be modelled by the function
D= 3 sin ( 0.49t - 0.6 ) + 6 t less and equal than 13
Where radians have been used.
Select two options which are true:
-The largest depth is 9 metres
-The smallest depth is 6 metres
-The time between the two high tides is exactly 12 hours
-At midnight the depth is approximately 4.3 metres
-The model can be used to predict the tide for up to 13 days
-The depth of water in the harbour falls after midnight
-At midday the depth is approximately 9 metres
Please explain your answer.
The largest depth is 9 metres.
The time between the two high tides is exactly 12 hours
D' derivative of D w.r.t D
D' =0 if
`t=4.43 ` gives max depth