| 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 |