So I have a function which represents motion. This function is x^2 which is also the area of a square. Now, what I know from the calculus is that the derivative is 2x, no arguing there but the derivative of a squares area is the perimeter, which is 4x? 4x and 2x are not the same at all! Another thing I wanted to bring up is that if this function is increasing two feet per second( if you do the math and anylitically look at the points you will see that you gain an extra two feet per second) or accelerated two feet per second per second then why at point 1,1 is my velocity or derivative two feet per second if at 1,1 you haven't even traveled two feet, you have only traveled one foot in one second? Please answer both questions for me somebody. Thank you.