Consider the differential equation d³x/dt³ +10 d²x/ dt² + 31 dx/dt + 30x ⁽¼⁾ = f(x), where f(x) is the input and is a function of the output, x. If f(x) = (1/4) eˣ, linearize the differential equation for x near 0.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 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)