has discontinuous derivative and which vanishes arbitrarily close to . These critical points are local max/min points of so is not one-to-one (and not invertible) on any interval containing . Intuitively, the slope does not propagate to nearby points, where the slopes rapidly oscillate between -1 and 3 (approximately).

If the derivative is continuous but zero at a point, the function is no longer necessarily locally injective. A real function that is locally constant at a point