This was my "ah-ha" moment as well. I always knew that derivative of the lowest point is 0 but I didn't really understand what it meant. Take any arbitrary curv

This was my "ah-ha" moment as well. I always knew that derivative of the lowest point is 0 but I didn't really understand what it meant. Take any arbitrary curve. Tangent is a line that touches a single point on the curve. Draw a tangent aka pencil touching the lowest point of the curve. It's derivative ie dy/dx apply the formulae to the curve's formulae. It will always be 0 which means it will have no "slope" ie parallel to the x axis