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Most of the curves you encounter in AP Calculus will be both continuous and differentiable. But we can run into problems if it turns out that it doesn't fit both conditions! Brush up on the rules for continuity with this guide Confirming Continuity over an Interval. This aspect of Differentiability And Continuity Iacedcalculuscom plays a vital role in practical applications.
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Furthermore, simply put, differentiable means the derivative exists at every point in its domain. Consequently, the only way for the derivative to exist is if the function also exists (i.e., is continuous) on its domain. Thus, a differentiable function is also a continuous function. This aspect of Differentiability And Continuity Iacedcalculuscom plays a vital role in practical applications.
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