Question

What are the absolute extrema of `f(x)= x-ln(3x) in [1,e]`?

Answer 1

Find the roots of first derivative you get

`f'(x)=0=>1-1/x=0=>x=1`

But `f''(x)=1/x^2>0`

Hence `f(1)=1-ln3` is a minimum.

Hence `f(e)>f(x)` for every `x` in `[1,e]` its a maximum

where `f(e)=e-ln(3e)`