A Particle moves along the x-axis so that its velocity at time t, for 0

Question

A Particle moves along the x-axis so that its velocity at time t, for 0<t<6, is given by a differentiable function v. The velocity is 0 at t = 0, t=3, and t=5, and the graph has horizontal tangents at t=1 and t=4. The areas of the regions bounded by the t-axis and the graph of v on the intervals [0, 3] [3, 5] and [5, 6] are 8, 3, and 2 respectively. At time t=0, the particle is at x=-2. 
a) for  0<t<6, find both the time and the position of the particle when the particle is farthest to the left. 
b) For how many values of t, where  0<t<6, is the particle at x=-8?

anonymous · Answer

c) On the interval 2<t<3, is the speed of the particle increasing or decreasing?

d) during what time intervals, is the acceleration of the particle negative?