| Input |
|---|
| x^3 – 3 x |
| Polynomial discriminant |
| Delta = 108 |
| Derivative |
| d/dx(x^3 – 3 x) = 3 (x^2 – 1) |
| Indefinite integral |
| integral (-3 x + x^3) dx = x^4/4 – (3 x^2)/2 + constant |
| Local maximum |
| max{x^3 – 3 x} = 2 at x = -1 |
| Local minimum |
| min{x^3 – 3 x} = -2 at x = 1 |
| Definite integral area below the axis between the smallest and largest real roots |
| integral_(-sqrt(3))^(sqrt(3)) (-3 x + x^3) theta(3 x – x^3) dx = -9/4 = -2.25 |
| Definite integral area above the axis between the smallest and largest real roots |
| integral_(-sqrt(3))^(sqrt(3)) (-3 x + x^3) theta(-3 x + x^3) dx = 9/4 = 2.25 |