Rolle's Theorem

A continuous differentiable function is shown with end points [math]a \text b[/math] such that [math]f(a) = f(b)[/math]. One end point can be adjusted and the other one will be where the [math]y[/math] values are equal. The plus symbols can be adjusted on the [math]x[/math]-axis. Orange diamonds show the location where the derivative is zero, [math]f'(x) = 0[/math] The function can be modified with the small black circles.

Any time the domain is not empty at least one diamond should appear. This indicates a zero derivative.