one-sided derivative, its interpretation

[gefest_md]

The situation which follows I could not find in (school) textbook. Let be the function $f\colon[0,\,+\infty)\to\mathbb{R}$:

$$f(x)=\left\{ \begin{array}{rl} 1 & \mbox{if $x=0$}\\ \sqrt{x} & \mbox{if $x>0$.} \end{array}\right.}$$

Then right derivative at $x=0$ is

$$f_r^\prime (x)=\lim_{x\rightarrow +0}{\frac{\sqrt{x}-1}{x}}=-\infty$$

What is then the geometric interpretation of this?