First and second derivatives as slopes of tangent lines
- Author:
- Marc Renault
This figure starts with a function graphed and a blue point on the -axis.
By dragging the blue point and selecting various options, you can see that the values of the first derivative are really the slopes of tangent lines to the graph of . Similarly, the values of the second derivative are really the slopes of tangent lines to the graph of .
See if you can make this observation with the figure: where the graph of curves above its tangent line is positive, and where the graph of curves below its tangent line is negative.