Here is a GIF demonstrating the tangent line as a point traverses a curve: https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1862/2017/

Here is a GIF demonstrating the tangent line as a point traverses a curve: https://s3-us-west-2.amazonaws.com/courses-images/wp-content/uploads/sites/1862/2017/06/23162553/of-sliding-derivative-line.gif https://s3-us-west-2.amazonaws.com/courses-images/wp-content... The "pencil" (the short line representing the tangent) is green when positive, black when zero, and red when negative. Note that when it is black/zero, the "pencil" line is flat. This occurs at both local maxima and minima.