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- Thread starter bubblewrap
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In summary, the conversation discusses the concept of differentiability in closed and open intervals, specifically the fact that a function can be differentiable more in an open interval than in a closed interval. This is due to the fact that a function may not be differentiable at the endpoints of a closed interval. An example is given with the function f(x)=x^(4/3) restricted to [0,1], which can be differentiated twice in the open interval (0,1) but only once at x=0. The conversation concludes with finding a function that is twice differentiable at both endpoints of a closed interval.

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bubblewrap said:

What is its second derivative? And can you evaluate it in ##0##?

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Oh is it because it can't be defined at ##x=0## that it's not differentiable at that point? Making it only twice differentiable in the open interval

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