\"\"

\

The function is \"\", \"\".

\

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 \"\".

\

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

\

Differentiate \"\" on each side with respect to \"\".

\

\"\"

\

\"\".

\

\"\" is not differentiable at \"\".

\

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

\

Then \"\".\"\"

\

From the mean value theorem :

\

\"\"

\

\"\".

\

Substitute \"\" in \"\".

\

\"\"

\

\"\"

\

\"\"

\

\"\"

\

\"\" 

\

\"\"

\

Rationalize the denominator with \"\".

\

\"\"

\

\"\"

\

\"\".