$\"\"$

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

Find the value of $\"\"$ and $\"\"$ and the concavity of the function.

Consider $\"\"$ .

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

$\"\"$ .

Consider $\"\"$ .

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

$\"\"$ .

Rewrite $\"\"$ .

$\"\"$ .

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

$\"\"$ .

$\"\"$

Find the value of $\"\"$ .

Rewrite the function.

$\"\"$

Substitute $\"\"$ .

$\"\"$

The Quotient rule of the derivative : $\"\"$ .

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

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

$\"\"$

$\"\"$ .

$\"\"$

For finding the concavity of the function equate $\"\"$ .

$\"\"$

The function is $\"\"$

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

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

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

$\"\"$

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

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