Question

f:(0,+infinite)=>R, f(x)=x*lnx
show that the function f is increasing on [1/e,+infinite)

Answer 1

finding its derivative:
f'(x)=Lnx+1
function is increasing if this derivative is grater tan 0. This means that Lnx have to be grater than -1. Solving lnx=-1 will give you the value of x for which the function starts to grow.