The function is .

Rewrite the function as .

Differentiate the function with respect to .

Recall the derivative of the exponential function : .

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Find extrema by equating the first derivative to zero.

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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 minimum at .

For inflection points, equate second derivative to zero.

Consider .

It is never possible, because and are never zero.

Hence the function has no inflection.

Graph :

Draw a coordinate plane.

Graph the function .

Observe the graph :

The function has the absolute minimum at .

There is no inflection points for .

The function has absolute minimum at .