Maximum and Minimum Distance

Maximum and Minimum Distance

If a moving point has position:

$$x=x(t)$$

then its distance from a fixed point $$a$$ is:

$$D=|x-a|$$

For differentiable motion away from $$x=a$$:

$$\frac{dD}{dt}=\frac{x-a}{|x-a|}\frac{dx}{dt}$$

Usage

- Used in optimization and related-rate problems involving distances.