関数計算機

この計算機は、1変数関数の定義域、値域、x切片、y切片、導関数、積分、漸近線、増加・減少の区間、臨界点（停留点）、極値（最小・最大、局所（相対）、絶対（大域））の点、凹凸の区間、変曲点、極限、テイラー多項式、およびグラフを求めようとします。区間の指定も可能です。偶奇性も判定します。

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.

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