Differentiability implies ___________________
continuity
Differentiability implies the existence of the derivative of a function at a certain point. In particular, if a function is differentiable at a point, it means that the limit of the difference quotient (i.e., the ratio of the change in the function value over the change in the independent variable) exists as the change in the independent variable approaches zero. This limit is interpreted as the slope of the tangent line to the graph of the function at that point. Differentiability is a stronger condition than continuity, and it guarantees that the function is locally linear around that point.
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