The Wikipedia article on numerical differentiation mentions the formula

$$ h=\sqrt \epsilon \times x $$

where $\epsilon$ is the machine epsilon (approx. $2.2\times 10^{-16}$ for 64-bit IEEE 754 doubles), to calculate the optimum "small number" $h$ to be used in differentiation, such as $$ \frac{f(x+h)-f(x)}{h} $$ But what if $x$ is zero? Then $h$ will be zero too, and division by zero is certainly not a way to do numerical differentiation. Is the article wrong? Is it otherwise correct, except that near zero (how near?) some small enough constant (how small?) should be used?