Differentiability implies ___________________
continuity
Differentiability implies that a function has a well-defined derivative at a given point or over an interval. In other words, if a function is differentiable at a point x, then it means that the function changes smoothly as x changes in its domain at that point, and thus has a tangent line or linearity property. Specifically, it implies that as the input x approaches the given point, the output smoothly approaches a certain value, rather than jumping or oscillating. In addition, differentiability also implies that the function is continuous at that point, since a function cannot be differentiable at a point where it is not continuous.
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