$\"\"$

The function is $\"\"$ .

Rewrite the function as $\"\"$ .

Differentiate the function with respect to $\"\"$ .

$\"\"$ .

Recall the derivative of the exponential function : $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

Find extrema by equating the first derivative to zero.

$\"\"$

Substitute the $\"\"$ value in original function.

$\"\"$

The function has extrema at $\"\"$ .

$\"\"$

Determine nature of the extrema, using second derivative test.

Consider $\"\"$ .

Apply derivative with respect to $\"\"$ .

$\"\"$ .

$\"\"$

$\"\"$ .

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

Point	Sign of $\"\"$
$\"\"$	\ $\"\"$ \

The absolute maximum at $\"\"$ .

$\"\"$

For inflection points, equate second derivative to zero.

$\"\"$

Inflection points :

Inflection point at $\"\"$ .

$\"\"$

Inflection point at $\"\"$ .

$\"\"$

Inflection points are $\"\"$ and $\"\"$ .

$\"\"$

Graph :

Draw a coordinate plane.

Graph the function $\"\"$ .

$\"\"$

Observe the graph :

The function has the absolute maximum at $\"\"$ .

Inflection points are $\"\"$ and $\"\"$ .

$\"\"$

The function has absolute maximum at $\"\"$ .

Inflection points are $\"\"$ and $\"\"$ .