Question

Find the maxima and minima of f (x) = $lo{g}_e$ x in [1, 3].

Answer 1

$f\left(x\right)=lo{g}_e^x$ is an increasing function in its domain $(x<0)$ as base is $>1$ $(e>1)$

$\therefore$ When $x\in [1,3]$

minimum occurs when $x=1$

i.e., minimum value of $f\left(x\right)=lo{g}_e^1=0$

maximum value occurs when $x=3$

i.e., maximum value of $f\left(x\right)=lo{g}_e^3$.