\"\"

\

The function is \"\".

\

Rewrite the function is \"\".

\

Apply first derivative on each side with respect to \"\".

\

\"\".

\

\"\".

\

\"\".

\

Apply second derivative on each side with respect to \"\".

\

\"\"

\

\"\"

\

\"\".

\

Determine the values of \"\" at which \"\" or \"\" does not exist.

\

\"\"

\

\"\"

\

\"\"

\

\"\"

\

\"\"  and \"\" and \"\".

\

\"\", \"\" and \"\".

\

The values of \"\" are \"\", \"\" and \"\".

\

\"\"

\

Test for concavity in the intervals \"\", \"\", \"\" and \"\".

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
IntervalsTest value \

Sign of \"\"

\
Conclusion
\"\" \

\"\"

\
\

\"\"

\
\

Concave upward

\
\"\"\"\"\"\"Concave downward
\"\" \

\"\"

\
\

\"\"

\
\

Concave upward

\
\"\" \

\"\"

\
\

\"\"

\
Concave downward
\

\"\"

\

The function is concave upward in the interval \"\" and \"\".

\

The function is concave downward in the interval \"\" and \"\".