Find the Critical Number(s) (If Any) and Test Them to Determine

question 133

Essay

Find the critical number(s) (if any) and test them to determine if $f ( x ) = \frac { x } { 1 - x ^ { 2 } }$ has a local maximum or local minimum or neither at each critical number.

---

Definitions:

Epicenter

The point on the Earth's surface directly above the focus of an earthquake, where the seismic waves are felt most strongly.

Seismograms

The recorded output of a seismograph, which shows the motion of the ground during an earthquake or other seismic event.

Nomogram

A graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a function.

Seismic Station

A facility equipped with instruments for detecting and recording earthquakes and other ground vibrations.