Calculadora de puntos críticos y extremos

Encuentra puntos críticos y extremos paso a paso

La calculadora intentará encontrar los puntos críticos (estacionarios), los máximos y mínimos relativos (locales) y absolutos (globales) de la función de variable única. El intervalo se puede especificar.

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.

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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.