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Calculadora de funciones

Calcular paso a paso las propiedades de una función

La calculadora intentará encontrar el dominio, rango, intersecciones x, intersecciones y, derivada, integral, asíntotas, intervalos de incremento y decremento, puntos críticos (estacionarios), puntos extremos (mínimo y máximo, local, relativo, absoluto y global), intervalos de concavidad, puntos de inflexión, límite, polinomio de Taylor y gráfica de la función de una sola variable. Se puede especificar el intervalo. También se determinará la paridad.

Enter a function of one variable:
Enter an interval:
Required only for trigonometric functions. For example, `[0, 2pi]` or `(-pi, 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 contact us.

Your input: find the properties of $$$f=x^{4} - 6 x^{2}$$$

Parity

The function is even.

Domain

$$$\left(-\infty, \infty\right)$$$

x-intercepts

$$$\left(0,0\right)$$$

$$$\left(\sqrt{6},0\right)\approx \left(2.44948974278318,0\right)$$$

$$$\left(- \sqrt{6},0\right)\approx \left(-2.44948974278318,0\right)$$$

y-intercepts

$$$\left(0,0\right)$$$

Range

$$$\left[-9, \infty\right)$$$

Critical Points

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

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

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

Intervals of Increase

$$$\left(- \sqrt{3}, 0\right) \cup \left(\sqrt{3}, \infty\right)\approx \left(-1.73205080756888, 0\right) \cup \left(1.73205080756888, \infty\right)$$$

Intervals of Decrease

$$$\left(-\infty, - \sqrt{3}\right) \cup \left(0, \sqrt{3}\right)\approx \left(-\infty, -1.73205080756888\right) \cup \left(0, 1.73205080756888\right)$$$

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

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

Global (Absolute) Minima and Maxima

For global minima and maxima, see extrema calculator.

Inflection Points

$$$\left(x, f \left(x \right)\right)=\left(-1,-5\right)$$$

$$$\left(x, f \left(x \right)\right)=\left(1,-5\right)$$$

Concave upward on

$$$\left(-\infty, -1\right) \cup \left(1, \infty\right)$$$

Concave downward on

$$$\left(-1, 1\right)$$$

Derivative

For derivative, see derivative calculator.

Integral

For integral, see integral calculator.

Asymptotes

For asymptotes, see asymptote calculator.

Limit

For limit, see limit calculator.

Taylor Polynomial

For Taylor polynomial, see taylor polynomial calculator.

Graph

For graph, see graphing calculator.