Step 1:

The function is $\"\"$ . $\"\"$

Domain: $\"\"$

The domain of a function is all values of $\"\"$ , those makes the function mathematically correct.

The domain of exponential functions is all real numbers.

The domain of $\"\"$ is all real numbers.

(2) Find the inflection points.

The function is $\"\"$ .

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

$\"\"$

$\"\"$ .

Again apply derivative on each side with respect to $\"\"$ .

$\"\"$

Apply product rule of derivatives $\"\"$ .

$\"\"$

$\"\"$ .

Find the inflection points.

Equate $\"\"$ to zero.

$\"\"$

The exponential function can not be zero.

$\"\"$

$\"\"$ .

The inflection point is at $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ .

The inflection point is $\"\"$ .

The inflection point is at $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ $\"\"$

$\"\"$ .

The inflection point is $\"\"$ .

The inflection points are $\"\"$ and $\"\"$ .

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

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

The function $\"\"$ is concave up on the interval $\"\"$ and $\"\"$ .

The function $\"\"$ is concave down on the interval $\"\"$ . \ \