$\"\"$

\

The function $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Find the relative extrema by equating the first derivative to zero.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ and $\"\"$ are not in the domain.

\

Substitute the $\"\"$ value in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Relative extrema at $\"\"$ . $\"\"$

\

Determine the nature of relative extrema, using second derivative test.

\

$\"\"$

\

Again apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Point

\"\"

Sign of

\"\"

\

\

$\"\"$

\

Conclusion

Relative minimum

\

The relative minimum at $\"\"$ . $\"\"$

\

Find the inflection points by equating the second derivative to zero.

\

$\"\"$ .

\

The second derivative of the function is never zero.

\

The second derivative is undefined at $\"\"$ .

\

The domain of the function is $\"\"$ .

\

$\"\"$ is not in the domain of the original function $\"\"$ .

\

Therefore, there are no inflection points.

\

$\"\"$

\

Graph:

\

Graph the function $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Relative minimum at $\"\"$ .

\

No inflection points.