Marginal R is dR/dt = R'(t)

R(t) = 2{5 -4cos[(pi/6)t]}

R'(t) = 2[(-4)(-sin[pi/6)t] *(pi/6)]

R'(t) = (8pi/6)sin[(pi/6)t]

When R'(t) = 0.

0 = (8pi/6)sin[(pi/6)t]

0 = sin[(pi/6)t]

(pi/6)t = arcsin(0)

(pi/6)t = 0, or 2pi

When (pi/6)t = 0,

t = 0 -----------------**

When (pi/6)t = 2pi,

t = (2pi)/(pi/6) = 12 ----**

Therefore, the marginal revenue is zero at week zero and week 12. ----answer.