I am having trouble with this problem. I thought that I knew what I was doing, but my answer does not agree with the given answer.
The position of a particle moving along a line is given by s(t) = 2t^3 - 24t^2 + 90t + 7 for t>=0. For what values of t is the speed of the particle increasing?
I thought that I would need the second derivative since acceleration would be needed to decide when speed was increasing. I found the second derivative to be s''(t) = 12t - 48. I set it equal to zero to find the critical point of t = 4. I tested on both sides and found that the acceleration is positive for t > 4. However, that does not match the given solution of 3 < t < 4 and t > 5.
Can anyone help explain to me what I am missing?
The position of a particle moving along a line is given by s(t) = 2t^3 - 24t^2 + 90t + 7 for t>=0. For what values of t is the speed of the particle increasing?
I thought that I would need the second derivative since acceleration would be needed to decide when speed was increasing. I found the second derivative to be s''(t) = 12t - 48. I set it equal to zero to find the critical point of t = 4. I tested on both sides and found that the acceleration is positive for t > 4. However, that does not match the given solution of 3 < t < 4 and t > 5.
Can anyone help explain to me what I am missing?
