Question

Locate any relative extrema and inflection points. Use a graphing utility to confirm your results.

y = x ln x

Answer 1

Step 1:

The function

Differentiate with respect to .

Apply Product rule in derivatives .

Step 2:

Find the relative extrema by equating the first derivative to zero.

Substitute the value in original function.

Substitute the value of  .

Relative extrema at .

Step 3:

Determine the nature of relative extrema, using second derivative test.

Apply derivative with respect to .

Point
Sign of
Conclusion	Relative minimum

The relative minimum at .

Step 4:

Find the inflection points by equating the second derivative to zero.

The second derivative of the function is never zero.

The second derivative is undefined at .

0 is not in the domain of the original function .

Therefore, there are no inflection points.

Step 5:

Graph:

.

Solution:

Relative minimum at .

No inflection points.