$\"\"$

$\"\"$ and $\"\"$ are concave upwards in the interval $\"\"$ .

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 $\"\"$ .

$\"\"$

Let the sum of two functions is $\"\"$ .

Let $\"\"$ be the number in the interval $\"\"$ .

$\"\"$

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

$\"\"$

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

$\"\"$

From the above given conditions $\"\"$ and $\"\"$ .

$\"\"$

From the second derivative test sum of two functions is also concave upwards in $\"\"$ .

$\"\"$

Sum of two functions is also concave upwards in $\"\"$ .