$\"\"$

The function is $\"\"$

Differentiate on each side with respect to $\"\"$ .

$\"\"$ ..

Product rule of derivatives : $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

The derivative function is $\"\"$ .

Again differentiate $\"\"$ on each side with respect to $\"\"$ .

$\"\"$ .

Product rule of derivatives : $\"\"$ .

$\"\"$

$\"\"$ .

Find the inflection point by equating $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ and $\"\"$ .

Inflection points:

(a) $\"\"$ at $\"\"$ .

$\"\"$ .

Inflection point $\"\"$ .

(b) $\"\"$ at $\"\"$ .

$\"\"$ .

Inflection point $\"\"$ .

$\"\"$

The test intervals are $\"\"$ , $\"\"$ and $\"\"$ .

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

\ \

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

$\"\"$

Inflection point $\"\"$ and $\"\"$ .

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

The graph is concave up in the interval $\"\"$ and $\"\"$ .