$\"\"$

The function is $\"\"$ .

Domain of the function is $\"\"$ .

Find the inflection points.

Differentiate $\"\"$ with respect to $\"\"$ .

$\"\"$ \ \

Differentiate $\"\"$ with respect to $\"\"$ .

$\"\"$ \ \

$\"\"$

Find the inflection points by equating $\"\"$ to zero.

$\"\"$

Thus, the inflection points are $\"\"$ .

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

$\"\"$ .

Therefore the inflection point is $\"\"$ .

$\"\"$

Consider the test intervals as $\"\"$ and $\"\"$ .

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

Concavity test:

(a) If $\"\"$ for all $\"\"$ in $\"\"$ , then the graph of $\"\"$ is concave upward on $\"\"$ .

(b) If $\"\"$ for all $\"\"$ in $\"\"$ , then the graph of $\"\"$ is concave downward on $\"\"$ .

Thus, the graph is concave up in the interval $\"\"$ .

The graph is concave down in the interval $\"\"$ .

$\"\"$

Inflection point is $\"\"$ .

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

The graph is concave down in the interval $\"\"$ .