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Calcolatore di funzioni
Calcola le proprietà di una funzione passo dopo passo
La calcolatrice proverà a trovare il dominio, l’immagine, le intersezioni con l’asse x, le intersezioni con l’asse y, derivata, integrale, asintoti, intervalli di crescita e decrescita, punti critici (stazionari), punti di estremo (minimi e massimi, locali, relativi, assoluti e globali), intervalli di concavità, punti di flesso, limite, polinomio di Taylor e il grafico della funzione a una variabile. L’intervallo può essere specificato. Verrà determinata anche la parità.
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.