The function f(x) = –0.5x2 + 16x – 96 can be used to trace the path of a rocket, where the x-axis represents the ground and the y-axis measures the height of the rocket. The mathematical domain of the function is all real numbers.

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)