x^6-6x^2+sqrt(3) - Wolfram|Alpha

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Input

x^6 - 6 x^2 + sqrt(3)

Plot

Plot

Plot

Alternate form

(x^4 - 6) x^2 + sqrt(3)

Polynomial discriminant

Δ_x = -39237696 sqrt(3)

Properties as a real function

Domain

R (all real numbers)

Range

{y element R : y>=sqrt(3) - 4 sqrt(2)}

Parity

even

Derivative

d/dx(x^6 - 6 x^2 + sqrt(3)) = 6 x (x^4 - 2)

Indefinite integral

integral(x^6 - 6 x^2 + sqrt(3)) dx = x^7/7 - 2 x^3 + sqrt(3) x + constant

Global minima

$min{x^6 - 6 x^2 + sqrt(3)} = sqrt(3) - 4 sqrt(2) at x = 2^(1/4)$

$min{x^6 - 6 x^2 + sqrt(3)} = sqrt(3) - 4 sqrt(2) at x = -2^(1/4)$

Local maximum

$max{x^6 - 6 x^2 + sqrt(3)} = sqrt(3) at x = 0$

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