horizontal cusp

A function f(x) has a spinode (also called a horizontal cusp) at a point x_0 if f(x) is continuous at x_0 and lim_(x->x_0) f'(x) = ∞ from one side while lim_(x->x_0) f'(x) = - ∞ from the other side, so the curve is continuous but the derivative is not.s

acnode | crunode | cusp | tacnode