Differentiable vs. Non-differentiable Functions

Differentiable and non-differentiable functions form essential components of mathematical analysis, each embodying distinct characteristics and behaviors. In calculus, differentiability signifies the smoothness of a function's graph, where the derivative exists at each point within its domain. Conversely, non-differentiable functions lack this property, exhibiting abrupt changes, corners, or vertical tangents, rendering them challenging to analyze using traditional differentiation methods. Understanding the disparities between these function types is fundamental in various fields, from optimization problems in engineering to modeling complex systems in physics and economics.