- #1
Joseph Nechleba
- 4
- 0
Using the standard equation of a circle x^2 + y^2 = r^2, I took the first and second derivatives and obtained -x/y and -r^2/y^3 , respectively. I understand that the slope is going to be different at each point along the circle, but what does not make sense to me is that the rate of change of the slope is dependent on the y value of a point along the circle. For some reason, I want to believe that, conceptually, the second derivative of a circle is a constant, which produces the "circle" shape. Can someone please clear my misunderstanding?