$\"\"$

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

Find the inflection points.

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

$\"\"$

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

$\"\"$

$\"\"$

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

$\"\"$

Therefore the function have inflection points at $\"\"$ and $\"\"$ .

$\"\"$

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

$\"\"$

The function have inflection points at $\"\"$ and $\"\"$ .

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

The graph is concave down in the intervals $\"\"$ and $\"\"$ .