2x^3-9x^2 - Wolfram|Alpha

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Input

2 x^3 - 9 x^2

Plot

Plot

Plot

Alternate form

x^2 (2 x - 9)

2 (x - 3)^3 + 9 (x - 3)^2 - 27

Roots

x = 0

x = 9/2

Polynomial discriminant

Δ = 0

Properties as a real function

Domain

R (all real numbers)

Range

R (all real numbers)

Surjectivity

surjective onto R

Derivative

d/dx(2 x^3 - 9 x^2) = 6 (x - 3) x

Indefinite integral

integral(2 x^3 - 9 x^2) dx = x^4/2 - 3 x^3 + constant

Local minimum

$min{2 x^3 - 9 x^2} = -27 at x = 3$

Local maximum

$max{2 x^3 - 9 x^2} = 0 at x = 0$

Definite integral

integral_0^(9/2) (-9 x^2 + 2 x^3) dx = -2187/32≈-68.3438

Definite integral area below the axis between the smallest and largest real roots

integral_0^(9/2) (-9 x^2 + 2 x^3) θ(9 x^2 - 2 x^3) dx = -2187/32≈-68.3438

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