Prove that the function $g(x) = \log x$ does not have any maxima or minima.

(N/A) Given the function $g(x) = \log x$.
First,we find the derivative of the function with respect to $x$:
$g'(x) = \frac{d}{dx}(\log x) = \frac{1}{x}$.
Since the domain of the logarithmic function $g(x) = \log x$ is $x > 0$,the derivative $g'(x) = \frac{1}{x}$ is always positive for all $x$ in its domain ($g'(x) > 0$ for all $x > 0$).
For a function to have a local maximum or minimum,there must exist a point $c$ in the domain such that $g'(c) = 0$ or $g'(c)$ does not exist.
In this case,$\frac{1}{x}$ is never equal to $0$ for any real value of $x$.
Since $g'(x) \neq 0$ for any $x$ in the domain,the function $g(x) = \log x$ does not have any points of local maxima or local minima.