Question

prove that f(x)=x-ln x is increasing for x>1

Answer 1

f'(x) = (1 - ln x)/x^2

Answer 2

critical point is 0
so x = e

Answer 3

f"(x) = (-3 + ln x)/x^3

Answer 4

Then you find out that the point is local maximum

Answer 5

oh okay, thank you (: