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13htran
for time 0<= t <= 10, a particle moves along the x-axis with position given by x(t) = t^3 - t^2 + 8t +5. A) During what time intervals is the speed of the particle increasing? B) What is the position of of the particle when it is farthest to the left?
For the increasing portion you only need to find the second derivative, and find out where it's positive. That will tell you a POSITIVE rate of change of the velocity, i.e,. increasing. Also, the position when it is furthest to the left is where v=0. So find where the derivative vanishes and then plug in to the position to see which one is furthest "left".