Скачать или смотреть Differentiability and Continuity (Piecewise Functions)

This Calculus 1 video explains differentiability and continuity of piecewise functions and how to determine if a piecewise function is continuous and differentiable. We work a couple of examples that show how to determine piecewise function continuity and piecewise function differentiability. For continuity, we show the need for the y values on the function to be the same at the x values where the graph of the piecewise function passes from one piece to the next. For differentiability, we also look at how to make sure that a piecewise function is differentiable at one of these x values, by checking to see if the derivatives of each piece are equal. Solving for unknowns in piecewise functions is also demonstrated in our examples.
0:00 Intro to piecewise functions continuity
1:14 Example 1 (Continuity)
3:20 Intro to piecewise functions differentiability
4:54 Example 2 (Continuity and differentiability)
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