Determine the longest interval in which the given initialvalue problemis certainto have a unique twicedifferentiable solution. Do not attempt to find the solutionty'' + 3y = t, y(1) = 1, y'(1) = 9

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)