This problem is from Khan Academy. Specifically for the blue point circled in red, the answer is that at this blue point, the object is neither speeding up nor slowing down. When I think about the rule about the signs of velocity and acceleration and what this means for change in speed, this makes sense: if velocity and acceleration and have the same sign, the object is speeding up, and if velocity and acceleration have opposite signs, the object is slowing down. At the blue point, the instantaneous velocity is zero and because zero is neither positive nor negative, the object is neither speeding up nor slowing down.
However, intuitively, this doesn't make sense. At the blue point circled in red, the velocity is zero so the speed must be zero. Also, the slope of the function at this blue point is negative so acceleration is negative, meaning that velocity is decreasing every second. If velocity is decreasing every second, then right after 6 seconds, the velocity will turn negative but the speed will have increased. So at the blue point, the object, even though it has zero speed, is in the process of speeding up. Why is this thinking wrong?