i think you do f'(x) and use the product rule?
f'(x) = x (1/x) + lnx (1)
1+lnx = 0
lnx = -1
ok i dont kow where to go from there.
THANKS IN ADVANCE!
$\displaystyle f'(x) = 1 + \ln{x} = 0$
$\displaystyle \ln{x} = -1$
$\displaystyle x = e^{-1} = \frac{1}{e}$
$\displaystyle f'(x) = 1 + \ln{x}$
$\displaystyle f''(x) = \frac{1}{x}$
$\displaystyle f''(x) > 0$ for all x in the domain of $\displaystyle f(x)$, so $\displaystyle f(x)$ is concave up everywhere, indicating $\displaystyle f\left(\frac{1}{e}\right)$ is a minimum.
value of the minimum is $\displaystyle f\left(\frac{1}{e}\right) = -\frac{1}{e}$