I am given a position equation
for t is greater than or equal to 0. I am asked to find the values of t where the speed is increasing.
If I'm correct, speed is the absolute value of velocity, which is the derivative of position. I got:
(not sure how to input absolute value symbol)
How do I know where the speed is increasing without plugging it into the calculator? To find where velocity increases, I found the zeros and then used a sign line, but I don't think that works for speed...or does it?
My bad. If you are looking for the intervals where speed is increasing then you need to find the derivative of speed which is the a(t). All finding the zeros of the velocity function will do is to tell you where velocity is positive and negative. If you take the absolute value of the acceleration function (its a line so its easy to visualize), you'll see acceleration decreasing from like 0 to 3 (or somewhere around there), and increasing from then on (assuming the thing doesn't stop.