Input
x^3 – 2 x
Polynomial discriminant
Delta = 32
Derivative
d/dx(x^3 – 2 x) = 3 x^2 – 2
Indefinite integral
integral (-2 x + x^3) dx = x^4/4 – x^2 + constant
Local maximum
max{x^3 – 2 x} = (4 sqrt(2/3))/3 at x = -sqrt(2/3)
Local minimum
min{x^3 – 2 x} = -(4 sqrt(2/3))/3 at x = sqrt(2/3)
Definite integral area below the axis between the smallest and largest real roots
integral_(-sqrt(2))^(sqrt(2)) (-2 x + x^3) theta(2 x – x^3) dx = -1
Definite integral area above the axis between the smallest and largest real roots
integral_(-sqrt(2))^(sqrt(2)) (-2 x + x^3) theta(-2 x + x^3) dx = 1