👉 In mathematics, a scarpment is defined as a point on a curve that is not a local extremum. It can be thought of as a limit point in calculus or a point where the derivative vanishes at a rate approaching zero. For example, consider the function f(x) = x^3 - 2x^2 + 1. At x = 0, f(0) = 0, but the derivative df/dx = 6x - 4x