$\"\"$

The function is $\"\"$ .

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

$\"\"$

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.

$\"\"$

The inflection points are $\"\"$ and $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Therefore the inflection points are $\"\"$ and $\"\"$ .

$\"\"$

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

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

The function is concave upward in the intervals $\"\"$ and $\"\"$ .

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

$\"\"$

The inflection points are $\"\"$ and $\"\"$ .

The function is concave upward in the intervals $\"\"$ and $\"\"$ .

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