The function  is an odd function and it is differentiable everywhere.

Mean value theorem :

Let  be a function that satisfies the following three hypotheses.

1.  is continuous on .

2.  is differentiable on .

Then there is a number  in  such that .

The function  is a differentiable on .

Odd function : If  is an odd function then .

A number  exists in the interval .

From the mean value theorem :

For a function  as a odd function , when a number  exist in the interval  then .

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