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Partial Differential Equation
Derivative
d/dx(3 x^3 + 2 x) = 9 x^2 + 2
Plot
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