# Math Help - f(x) = xlnx. the minimum value attained by f is...

1. ## f(x) = xlnx. the minimum value attained by f is...

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.

2. $f'(x) = 1 + \ln{x} = 0$

$\ln{x} = -1$

$x = e^{-1} = \frac{1}{e}$

$f'(x) = 1 + \ln{x}$

$f''(x) = \frac{1}{x}$

$f''(x) > 0$ for all x in the domain of $f(x)$, so $f(x)$ is concave up everywhere, indicating $f\left(\frac{1}{e}\right)$ is a minimum.

value of the minimum is $f\left(\frac{1}{e}\right) = -\frac{1}{e}$