Criterios de derivabilidad

Criterios de derivabilidad, or criteria of differentiability, refer to the conditions that determine whether a function can be smoothly "turned" at a certain point, meaning it has a derivative there. In simple terms, if a function is smooth enough around that point—no sharp corners or jumps—it satisfies these criteria and is considered differentiable. Mathematically, this involves examining limits and whether the function's rate of change approaches a specific value as you get closer to the point. These criteria ensure the function behaves predictably and smoothly, which is essential in calculus for analyzing and understanding changes.