- #1

#### SlowLearner1218

Ok so as I have learned this past summer semester that a derivative is the slope of a tangent line or a single point in a function or basically the instantaneous rate of change. I looked up some YouTube videos and came to understand that it's not exactly a single point but rather the difference between 2 points that are so so close to each other that they're basically taken as a single point. So I'd like to know if I have this right. The derivative is the rate of change between two points that are close to each other in proximity that the distance between them inches them closer and closer to zero but never ACTUALLY the same position because at that point there wouldn't be 2 points to compare.

So if I have the previous statement above correct my next question is this. Am I interpreting this right in that time derivative in an acceleration graph means the very very small distance, almost zero but never quiet zero, between two points in the x axis? If interpretation is correct then the time derivative would not equal the acceleration right? Since time derivative is only talking about the change in the x-axis and acceleration is the change of y-axis over the change in the x axis.