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