Depth of the water as a function of time  is .

Where  is time in hours after the midnight.

Tide rising or falling with respect to time is .

Consider .

Differentiate on each side with respect to .

(a)

When time  AM :

Tide rising or falling with respect to time  is .

Substitute  in above expression.

Therefore tide is rising with a speed of  m/hr.

(b)

When time  AM :

Substitute  in above expression.

Therefore tide is rising with a speed of   m/hr.

(c)

When time  AM :

Substitute  in above expression.

Therefore tide is falling with a speed of   m/hr.

(d) At Noon :

That means the time is  PM:

Substitute  in above expression.

Therefore tide is falling with a speed of   m/hr.

(a) The tide is rising with a speed of   m/hr.

(b) The tide is rising with a speed of   m/hr.

(c) The tide is falling with a speed of   m/hr.

(d) The tide is falling with a speed of   m/hr.