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Rate of Change

Derivative

d/dx(3 x^3 + 2 x) = 9 x^2 + 2

Plots

Geometric figure

parabola

Alternate form

(sqrt(2) - 3 i x) (sqrt(2) + 3 i x)

Complex roots

x = -(i sqrt(2))/3

x = (i sqrt(2))/3

Roots in the complex plane

Polynomial discriminant

Δ = -72

Properties as a real function

R (all real numbers)

{y element R : y>=2}

even

Indefinite integral

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

Global minimum

$min{9 x^2 + 2} = 2 at x = 0$