Question

Let f(x)=xlnx. The minimum value attained by f is..
the answer is -1/e .
Please explain how to get to this answer.

Answer 1

This is a classic "extreme value" problem.
1. Find the derivative, (dy/dx), of y=x ln x. (That's y = (x)(ln x).)
2. Set this derivative = to zero and solve for the "critical value."
3. Determine whether you have a minimum or a max at that x-, or critical, value.
Questions? Please ask.