(8)

\

Step 1:

\

Concavity test :

\

If $\"\"$ for all $\"\"$ in the interval, then the graph of f is concave upward on the interval.

\

If $\"\"$ for all $\"\"$ in the interval, then the graph of f is concave downward on the interval.

\

Observe the graph $\"\"$ .

\

$\"\"$ over the intervals $\"\"$ and $\"\"$ , therefore the function $\"\"$ is concave upward on the intervals $\"\"$ and $\"\"$ .

\

$\"\"$ over the intervals $\"\"$ and $\"\"$ , therefore the function $\"\"$ is concave downward on the intervals $\"\"$ and $\"\"$ .

\

Solution :

\

The function $\"\"$ is concave upward over the intervals $\"\"$ and $\"\"$ .

\

The function $\"\"$ is concave downward over the intervals $\"\"$ and $\"\"$ .

\

\

(9)

\

Step 1:

\

Concavity test :

\

If $\"\"$ for all x in the interval, then the graph of f is concave upward on the interval.

\

If $\"\"$ for all x in the interval, then the graph of f is concave downward on the interval.

\

Observe the graph $\"\"$ .

\

$\"\"$ over the intervals $\"\"$ and $\"\"$ , therefore the function $\"\"$ is concave upward on the intervals $\"\"$ and $\"\"$ .

\

$\"\"$ over the interval $\"\"$ , therefore the function $\"\"$ is concave downward on the interval $\"\"$ .

\

Solution :

\

The function $\"\"$ is concave upward over the intervals $\"\"$ and $\"\"$ .

\

The function $\"\"$ is concave downward over the interval $\"\"$ .