\"\"

\

The function is \"\".

\

Apply first derivative with respect to \"\".

\

\"\"

\

Apply second derivative with respect to \"\".

\

\"\"

\

The values of \"\" is \"\".

\

\"\"

\

Test for concavity in the intervals \"\" and \"\", as shown in the below table.

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

Sign of \"\"

\ 		Conclusion
\"\"\"\" \

\"\"

\ 		Concave upward
\"\" \

\"\"

\ 		\"\"Concave downward
\

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

\

Concave down in the interval \"\".

\

\"\"

\

Concave upward in the interval \"\". 

\

Concave down in the interval \"\".