Critical Points of a Cubic Function

This visualization shows the cubic function f(x) = x³ − 6x² + 9x + 2, its derivative, and how critical points arise where the derivative is zero. The exact critical points of this function are x = 1 (local maximum) and x = 3 (local minimum). Use the widgets to move along the curve, magnify the region, and reveal the derivative to see how the sign of f′(x) determines the type of critical point.