Input
x^3 – 4 x
Polynomial discriminant
Delta = 256
Derivative
d/dx(x^3 – 4 x) = 3 x^2 – 4
Indefinite integral
integral (-4 x + x^3) dx = x^4/4 – 2 x^2 + constant
Local maximum
max{x^3 – 4 x} = 16/(3 sqrt(3)) at x = -2/sqrt(3)
Local minimum
min{x^3 – 4 x} = -16/(3 sqrt(3)) at x = 2/sqrt(3)
Definite integral area below the axis between the smallest and largest real roots
integral_(-2)^2 (-4 x + x^3) theta(4 x – x^3) dx = -4
Definite integral area above the axis between the smallest and largest real roots
integral_(-2)^2 (-4 x + x^3) theta(-4 x + x^3) dx = 4