The volume of fuel in a tank changes at a rate given by the equation v'\left(t\right)=\frac{4t}{\sqrt[3] {t^2+3}},\: t\ge0 v ′ ( t ) = 4 t t 2 + 3 3 , t ≥ 0 at t=\sqrt{[\textbf{d}]} t = [ d ] hours the tank holds 9.[\textbf{b}] 9. [ b ] gallons. what is the volume of fuel in the tank after [\textbf{c}] [ c ] hours? round answer to one decimal place.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)