f(x)=-8xlnx decreases over what domain

Answer 1

f'(x) = -8x(1/x ) + (-8)lnx
= -8 - lnx
to be decreasing, -8 - 8lnx < 0
8lnx + 8 > 0
8 lnx > -8
lnx > -1

(solve lnx = -1, x = 1/e

which is true for all x > 1/e