The graph of [math]f(x)[/math] is shown in black. Its curvature function [math]k(x)[/math] is shown in red.[br][br]Drag the slider to change [math]a[/math], the x-value of point A (where the osculating circle to f is shown). You can also change [math]f(x)[/math] using the input box.[br][br]Additional functions:[br][math]n(x)[/math] = normal line when x=a[br][math]p(x)[/math] = x-coordinate of osculating circle when x=a[br][math]q(x)[/math] = y-coordinate of osculating circle when x=a[br][math]c(x)[/math] = scalar used in calculation of center of osculating circle: [math] \langle p(a), q(a) \rangle = \langle a, f(a) \rangle + c(a) \langle f'(a), -1 \rangle [/math]