\"\"

\

The function is \"\".

\

Mean value theorem :

\

Let \"\" be a function that satisfies the following hypotheses :

\

1. \"\" is continuous on \"\".

\

2. \"\" is differentiable on \"\".

\

Then there is a number \"\" in \"\" such that \"\".

\

\"\"

\

The function is \"\".

\

The function is  continuous on the interval \"\".

\

Differentiate \"\" with respect to \"\".

\

\"\"

\

\"\".

\

The function is differentiable on the interval \"\".

\

The mean value theorem satisfies the hypothesis.

\

Then \"\"

\

\"\"

\

From the mean value theorem :

\

\"\"

\

\"\".

\

Substitute \"\" in \"\".

\

\"\"

\

\"\"

\

\"\"

\

\"\"

\

\"\" 

\

\"\"

\

Substitute \"\" in \"\".

\

\"\" and \"\".

\

\"\"

\

\"\" and \"\".