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: