Скачать или смотреть WHEN is a PIECEWISE defined function continuous/differentiable? | Calculus Tutorial

We explain how to test continuity and differentiability at a point where different pieces of a piecewise-defined function merge. In particular, we study the left-hand limit and the right-hand limit, and the left-hand derivative and the right-hand derivative. In the example in the thumbnail, we use the continuity and the differentiability at x = 1 separately in order to set up two simultaneous equations for a and b. Finally, we solve the simultaneous equations to determine the unique values of a and b such that the function is differentiable (at x = 1, and in general).

The techniques in this video generally illustrate how to determine continuity and differentiability of a function at a point. A mastery of this concept is central to problems that arise in homework, assignments, tests and exams in high school and college calculus.

If you enjoy this video, I would love if you could please like ✅ , subscribe 🎉, and share ⏩ with students, classmates, friends and family - it means so much to help support me in my goal of creating elite infinite free accessible math education worldwide! 😊 If you would like to support my channel beyond this (which of course would mean so much to me 🤗), please check out my "Buy me a Coffee" and my "Patreon" page!

Buy me a Hot Chocolate 😊: https://buymeacoffee.com/math_mastery... ☕️

Become a Patreon Member 🤩:   / mathmasterywithamitesh