# What are the values and types of the critical points, if any, of #f(x)=xlnx#?

##### 1 Answer

Local minimum:

#### Explanation:

Take the first derivative, noting that the domain of the original function is

The domain of the first derivative is also

Set to zero and solve for

Recalling that

This is not a very complex function, so we can take the second derivative and apply the Second Derivative Test, which tells us that if

Thus, we have a local minimum at

Local minimum: