On the problem of function differentiability, is it required that the left and right derivatives are equal and equal to the derivatives at x0? Or is it only necessary that the left and right derivatives are equal? Or if it is a removable discontinuity point, it means that this derivative does not exist, but this derivative is differentiable?

On the problem of function differentiability, is it required that the left and right derivatives are equal and equal to the derivatives at x0? Or is it only necessary that the left and right derivatives are equal? Or if it is a removable discontinuity point, it means that this derivative does not exist, but this derivative is differentiable?

As long as the left and right derivatives exist and are equal, the derivative at x0 must be the same as the left and right derivatives
At least one of the left and right derivatives at the removable discontinuity does not exist
I think you've confused the left and right derivatives with the left and right limits of derivatives
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