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Twice-differentiable simply means that the function can be differentiated twice. eg. If y = x^5 (^5 means to the power of 5). Then y' = 5x^4 (i.e. differentiating once) Then y'' = 20x^3 (differentiating twice)
No.
In basic terms, Calculus is Differentiation and Integration And all things associated with that.
In its simplest form, l'Hôpital's rule states that for functions f and g which are differentiable on I\ {c} , where I is an open interval containing c:If, and exists, and for all x in I with x ≠ c,then.^from wiki
I don't think such a term is used in calculus. Check the spelling. Perhaps you mean point of inflection?