Drag point [math]P[/math] and see how the slope of the tangent to [math]f[/math] at [math]P[/math] changes. This slope is the [b]derivative of [math]f[/math] at [math]x=a[/math][/b], where [math]a[/math] is the [math]x[/math]-coordinate of [math]P[/math]. Point [math]Q[/math] has the same [math]x[/math]-coordinate as [math]P[/math], and its [math]y[/math]-coordinate is the slope of the tangent line at [math]P[/math].

What is the graph of the function determined by all possible locations of point [math]Q[/math]? This function is the [b]derivative of [math]f[/math][/b]. Try a different function and repeat.