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Derivatives and Differentiability of a Function

The derivative as the slope of a function at a point, what it means for a function to be differentiable everywhere versus to have a kink where no single slope exists, and how the slope's sign and magnitude indicate which direction reduces the function's value.

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Continuity and Differentiability in Calculus

Continuity and differentiability in calculus describe the smoothness and structural integrity of functions over a domain; continuity is defined by the existence of limits equal to function values, wh…