A function is said to have its 'critical points' when
its derivative is 0 or the derivative does not exist. In terms of
geometric appeareance, that means the slope of a line tangent to
the function does not exist (if the derivative does not exist),
or is either horizontal or vertical.

The critical points are found by finding the roots of the first derivative equation. In this example we look for the critical points of the function:

$f\left(x\right)={x}^{4}-8{x}^{2}+3$

The critical points are found by finding the roots of the first derivative equation. In this example we look for the critical points of the function:

$f\left(x\right)={x}^{4}-8{x}^{2}+3$

Critical Points

Electric Book-Link (e-Blink) URL:

The URL listed above can be inserted into your postings or e-mails; it will point to the text or area of the graph that you have selected.

To insert the link:

- Drag your mouse across any text in the green problem area, or
- Drag your mouse to form a selection box on the green graph area
- Open the e-Blink tab to display this tab.
- Copy the text above to your clipboard
- When editing a note to your community or editing your e-mail, select some text and press the link button.
- Paste your link into the text box for the URL.