Differentiability refers to the property of a function that indicates whether it has a defined derivative at a certain point or throughout an interval. A function is differentiable at a point if it is smooth enough for the tangent line to be well-defined, meaning that small changes in the input result in small changes in the output. This concept is crucial for analyzing nonlinear systems and optimizing functions, as it helps in determining where functions change and allows for the application of methods that rely on derivatives.
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