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Critical Points and Extrema Calculator

Find critical points and extrema step by step

The calculator will try to find the critical (stationary) points, the relative (local) and absolute (global) maxima and minima of the single variable function. The interval can be specified.

Enter a function of one variable:
Enter an interval:
Required only for trigonometric functions. For example, `(-2pi, 3pi)` or `[pi/2, oo)`. If you need `oo`, type inf.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your input: find the local and global minima and maxima of $$$f=x^{4} - 6 x^{2}$$$

Critical Points

$$$\left(x, f \left(x \right)\right)=\left(- \sqrt{3},-9\right)\approx \left(-1.73205080756888,-9\right)$$$

$$$\left(x, f \left(x \right)\right)=\left(0,0\right)$$$

$$$\left(x, f \left(x \right)\right)=\left(\sqrt{3},-9\right)\approx \left(1.73205080756888,-9\right)$$$

Global (Absolute) Minima

$$$\left(x, f \left(x \right)\right)=\left(- \sqrt{3},-9\right)\approx \left(-1.73205080756888,-9\right)$$$

$$$\left(x, f \left(x \right)\right)=\left(\sqrt{3},-9\right)\approx \left(1.73205080756888,-9\right)$$$

Global (Absolute) Maxima

No global maxima.

Local Minima

$$$\left(x, f \left(x \right)\right)=\left(- \sqrt{3},-9\right)\approx \left(-1.73205080756888,-9\right)$$$

$$$\left(x, f \left(x \right)\right)=\left(\sqrt{3},-9\right)\approx \left(1.73205080756888,-9\right)$$$

Local Maxima

$$$\left(x, f \left(x \right)\right)=\left(0,0\right)$$$

Graph

For graph, see graphing calculator.