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Funktionsräknare
Beräkna en funktions egenskaper steg för steg
Kalkylatorn kommer att försöka hitta definitionsmängd, värdemängd, x-skärningspunkter, y-skärningspunkter, derivata, integral, asymptoter, intervall där funktionen är växande respektive avtagande, kritiska (stationära) punkter, extrempunkter (minimum och maximum, lokala, relativa, absoluta och globala), konkavitetsintervall, böjpunkter, gränsvärde, Taylorpolynom och grafen för envariabelfunktionen. Intervallet kan anges. Funktionens paritet (jämn/udda) bestäms också.
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.