$\"\"$

\

The function $\"\"$ .

\

Consider $\"\"$ .

\

Differentiate with respect to $\"\"$ .

\

$\"\"$ .

\

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.

\

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

\

$\"\"$

\

$\"\"$

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

Point

Sign of

\"\"

\"\"

\

\

$\"\"$

\

\

The absolute maximum at $\"\"$ .

\

$\"\"$

\

For inflection points, equate second derivative to zero.

\

$\"\"$

\

$\"\"$

\

Inflection points:

\

$\"\"$

\

$\"\"$

\

Inflection points are $\"\"$ .

\

$\"\"$

\

Graph:

\

$\"\"$

\

Observe the graph the function has the absolute maximum at $\"\"$ .

\

$\"\"$

\

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