This figure starts with a function [math]f[/math] graphed and a blue point on the [math]x[/math]-axis.[br][br]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 [math]f[/math]. Similarly, the values of the second derivative are really the slopes of tangent lines to the graph of [math]f'[/math].[br][br]See if you can make this observation with the figure: where the graph of [math]f[/math] curves [i]above [/i]its tangent line [math]f''[/math] is positive, and where the graph of [math]f[/math] curves [i]below [/i]its tangent line [math]f''[/math] is negative.