Firstly, the separate pieces must be joined. That means the function must be continuous. Secondly, at each connection you need to look at the gradient on the left and the gradient on the right. If the left hand derivative equals the right hand derivative at each connection then the function is differentiable .
9 июл. 2022 г.
Videolar Most functions that are given are continuous in their domain, and functions that are not continuous are not differentiable. So functions given usually tend to ... |
16 февр. 2017 г. · As you have calculated, for the function to be continuous at x=1, we must have a+b=e. Now, if a+b=e, observe that f′(x)={ex,x<11x+2ax+b,x≥1. |
19 окт. 2016 г. · Piecewise functions may or may not be differentiable on their domains. To be differentiable at a point cx. = , the function must be continuous, ... |
2 окт. 2014 г. · A piecewise function can definitely be differentiable if (a) its pieces are differentiable and (b) it's differentiable at the points where they're joined. |
21 окт. 2014 г. · f is continuous at 0 means that limx→0+f(x)=limx→0−f(x)⟺0=A+B. Also, f is differentiable at 0 means that limx→0+f′(x)=limx→0−f′(x)⟺1=A. |
18 сент. 2022 г. · Every continuous piecewise function will "meet" as this one does, whether or not it is vertical there. But one that is differentiable will have ... |
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