Question

Prove that the following function does not have maxima or minima.

$g\left(x\right)=logx$

Answer 1

Given function is, $g\left(x\right)=logx\Rightarrow g^{\prime }\left(x\right)=\frac{1}{x}$
Since, log x is defined for a positive number x, then $g^{\prime }\left(x\right)>0$ for any x. Therefore, there does not exist any x belongs to R such that $f^{\prime }\left(x\right)=0$
Hence, function g does not have maxima or minima.