Step 1:

The function .

Consider .

Differentiate with respect to .

.

Recall the derivative of the exponential function .

.

Step 2:

Find extrema by equating the first derivative to zero.

Substitute the value in original function.

The function has extrema at .

Step 2:

Determine nature of the extrema, using second derivative test.

Apply derivative with respect to .

Point	Sign of
	\   \ \

The absolute maximum at .

Step 3:

For inflection points, equate second derivative to zero.

Inflection points:

Inflection points are .

Step 3:

Graph:

Observe the graph the function has the absolute maximum at .

Solution:

The function has absolute maximum at .