x - x^2 - Wolfram|Alpha

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Input

x - x^2

Alternate form

-x (x - 1)

(1 - x) x

1/4 - (x - 1/2)^2

Roots

x = 0

x = 1

Polynomial discriminant

Δ = 1

Properties as a real function

Domain

R (all real numbers)

Range

{y element R : y<=1/4}

Derivative

d/dx(x - x^2) = 1 - 2 x

Indefinite integral

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

Global maximum

$max{x - x^2} = 1/4 at x = 1/2$

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