The CriticalPoints(f(x), x) command returns all critical points of f(x) as a list of values.

The CriticalPoints(f(x), x = a..b) command returns all critical points of f(x) in the interval [a,b] as a list of values.

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

A critical point is defined as any point at which the derivative is either zero or does not exist.

If the expression has an infinite number of critical points, a warning message and sample critical points are returned.

The opts argument can contain the following equation that sets computation options.

numeric = true or false

Whether to use numeric methods (using floating-point computations) to find the critical points of the expression. If this option is set to true, the points a and b must be finite and are set to $\mathrm{-10}$ and $10$ if they are not provided. By default, the value is false.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right)\:$

$\mathrm{CriticalPoints}\left(3x^2-x\right)$

$\left[\frac{1}{6}\right]$

$\mathrm{CriticalPoints}\left(3x^5-5x^3+3\,x\right)$

$\left[\mathrm{-1}\,0\,1\right]$

$\mathrm{CriticalPoints}\left(2x^3+5x^2-4x\right)$

$\left[\mathrm{-2}\,\frac{1}{3}\right]$

$\mathrm{CriticalPoints}\left(2x^3+5x^2-4x\,x=0..1\right)$

$\left[\frac{1}{3}\right]$

$\mathrm{CriticalPoints}\left(\frac{x^2-3x+1}{x}\,x\right)$

$\left[\mathrm{-1}\,1\right]$

$\mathrm{CriticalPoints}\left(\frac{x^2-3x+1}{x}\,x\,\mathrm{numeric}\right)$

$\left[\mathrm{-1.000000000}\,1.000000000\right]$