if x*ln(x) = 0 then either x = 0 or ln(x) = 0 because if you have a product of two terms that yield zero, one or the other must be zero. however, we have that x > 0 (we need this for the log to be defined) so, you are correct, you are left with only one solution, x = 1.

good!Secondly for part b) I didnt think there were any maxima/minima because of what I said above. However, differentiating the function I get

lnx + x(1/x)

equating to zero gives

lnx + 1 = 0

lnx = -1

lnx = -lne

lnx = lne^-1

x = 1/e

yup. you're a genius!Plugging this into the second derivative (which is 1/x) gets me e as a minima.

Is this correct?

use integration by parts with andAnd for the last part it tells me to use integration by parts, but it doesnt get me anywhere...

you know what u and dv represent, right?