$\"\"$

The functions are $\"\"$ and $\"\"$ .

Find the value of $\"\"$ . \ \

Consider $\"\"$ .

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

$\"\"$ .

Consider $\"\"$ .

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

$\"\"$ . \ \

$\"\"$

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

$\"\"$ .

$\"\"$

Find the value of $\"\"$ . \ \

$\"\"$

Substitute $\"\"$ .

$\"\"$

Apply quotient rule of derivatives : $\"\"$ .

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

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

$\"\"$

$\"\"$ .

$\"\"$

Finding the concavity of the function by equating $\"\"$ .

$\"\"$

The function is $\"\"$ .

Split the interval into $\"\"$ , $\"\"$ and $\"\"$ .

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

Therefore, the function $\"\"$ is concave uopward in the interval $\"\"$ .

$\"\"$

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

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