Find a function that is differentiable at every point of an interval [a,b] but that the third derivative does not exist at any point

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So far we have looked at derivatives outside of the notion of differentiability The problem with this approach though is that some functions have one or many points or intervals where their derivatives are undefined A function f is differentiable at a point c if exists Similarly f is differentiable on an open interval a b if exists for every c in a b Basically f is differentiable at c if fc is defined by the above definition Another point of note is that if f is differentiable at c then f is continuous at c Lets go through a few examples and discuss their differentiability First consider the following function plot1x2 x 5 5showymin0 ymax10 Toggle Line Numbers To find the limit of the functions slope when the change in x is 0 we can either use the true definition of the derivative ... View the full answer