Mode of a Continuous Variable

A mode is a value of x at which the given density f(x) attains its greatest value on its support. From a sketch, identify the highest point or points of the density. The mode is an input value, not the height of the density. Using calculus, solve f (x)=0 on each differentiable piece, then compare density values at admissible stationary points, endpoints and joins. A stationary point need not be a maximum, and a maximum need not be stationary. Retain every value attaining the greatest density; if the density has a flat highest section, every value in that section is a mode.