A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=2/3t^3−5t^2+8t. Over the time interval 0<t<5, for what values of t is the speed of the particle increasing?

Answer 1

I did this on the graphing calculator. I saw the max is at x=1 and there is a min at x=4

0 to 1 increasing

1 to 4 decreasing

4 to 5 increasing

To find this using calculus, you would find the first derivative, set it equal to zero and solve. This would give you your critical values. Then you would use test points between each of the critical values. Where the test point is positive, it would be increasing, negative is would be decreasing.