Differentiability - AP® Calculus AB Definition

What is differentiability in AP® Calculus?

Differentiability is a fundamental concept in calculus that describes whether a function has a derivative at each point in its domain. A function that is differentiable is smooth and has a well-defined tangent line at every point.

For a function to be differentiable at a particular point, it must first be continuous there; however, continuity alone does not guarantee differentiability. Key characteristics of differentiability include the absence of sharp corners or cusps and the lack of vertical tangent lines.

In the context of AP® Calculus, understanding differentiability is essential for mastering the computation and application of derivatives, as it allows students to analyse and predict the behaviour of various functions.