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Differentiability and continuity

Differentiability and continuity

We explore the notion of differentiability at a point and its relationship with continuity, using the definition of a derivative. If a function is differentiable at x = c, then it is continuous at x = c. However, a function being continuous does not guarantee that it is differentiable, as demonstrated with an absolute value function.

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Differentiability at a point: graphical

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Differentiability at a point: algebraic (function is differentiable)

Differentiability at a point: algebraic (function is differentiable)

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Differentiation Examples

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