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Function Calculator

Calculate the properties of a function step by step

The calculator will try to find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical (stationary) points, extrema (minimum and maximum, local, relative, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single-variable function. The interval can be specified. Parity will also be determined.

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 write it in the comments below.

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.