Differentiability of Piecewise Functions - Calculus

In this video, I go through 3 examples, showing how to verify that a piecewise function is differentiable. I show a few different methods; I show how to check for differentiability graphically, using the limit definition of differentiability and through numerical analysis.

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[pratiksapkota]

Good explanation. Straight, comprehensive, no jargon

[autumnanddelusions]

straight to the point. That's what we need ! Thank you, man.

[Myheart]

You just earned a subscriber because you reply so well to the comments

[memoriessssssss]

Thank you so much! Your explanations were easy to comprehend and you got straight to the point! Wish I had you as my teacher!

[oldbengalivibes]

If you want to check continuity and differentiability just see this video.
Straight forward❤❤❤

[gsvwuyv]

5:32 here I didn’t really understand why we don’t put the equal, Is it something that I have to do every time or there is a specific thing that tells me if I need to?

[brunotumbana]

Thank you very much you made it easy for me. I really undertood. Thanks.

[LihleNgxeke]

Thank you sir you made it much more easy😊

[Steve-jioz]

Great explanation ! I have one question : In the last example, the reason for failing the differentiability test, is it because the limit does not prove that it is differentiable but if it were it would be equal to 1/2 ? If you use the epsilon-delta definition of the limit for the derivative, can you skip the continuity test ?

[Karo-]

i have a question isn’t it better to say derivative from the left and derivative from the right
(LHD=RHD) and not limit of derivative, because the limit of derivative doesn’t have to exist for a function to be differentiable at a certain point the left and right hand derivatives must be equal not necessarily the limits of derivatives

[chilufyamelissa]

Thank you, it's helpful.
But I have a question, what if you do the continuous part and you get the same values for the right and left side then for the differentiable part you find different values...

For example maybe you are given a f(x) = 4 if x<2
2x if x≥2

[TigKol]

Hello, why do we have to show that g(x) is continuous first

[ddaspires]

I have a doubt "differentiable then it is continuous" But why you are solving first continuous then differentiable any other specific reason for it can you explain me as soon as possible

[arestes]

I'm sorry to bump like this... but the way you try to prove that g is differentiable at x=2 at 5:50 is wrong. It assumes that the derivative is continuous. There are certainly derivatives that turn out not to be continuous, so the logic is faulty. I agree that most exam-like examples will succeed in checking the lateral limits of the derivative being equal, corresponding to the actual lateral limits of the increment quotient... but still, it's not the way to prove differentiability.