D(t)=10+4.9cos(pi/6 × t)

Question

D(t)=10+4.9cos(pi/6 × t)

D is defined above models the depth, in feet, of the water t hours after 12 am. Which of he following shows the method for finding the instantaneous rate of change of the depth of the water, in feet per hour, at 6 am ?

A) D(6) - D(0)/ 6-0 = -1.633

B) D'(6) = 0

C) D'' (6) = 1.343

D) D(6) = 5.100

Answer 1

D '(t) = -4.9sin(πt/6)(π/6)

D '(6) = -4.9sin(π)(π/6) = 0

So the answer is B) since sin(π)=0

A) is the average rate, not instantaneous rate.