4x^2-x-3
| Input |
|---|
| 4 x^2 – x – 3 |
| Geometric figure |
| parabola |
| Polynomial discriminant |
| Delta = 49 |
| Derivative |
| d/dx(4 x^2 – x – 3) = 8 x – 1 |
| Indefinite integral |
| integral (-3 – x + 4 x^2) dx = (4 x^3)/3 – x^2/2 – 3 x + constant |
| Global minimum |
| min{4 x^2 – x – 3} = -49/16 at x = 1/8 |
| Definite integral |
| integral_(-3/4)^1 (-3 – x + 4 x^2) dx = -343/96~~-3.57292 |
| Definite integral area below the axis between the smallest and largest real roots |
| integral_(-3/4)^1 (-3 – x + 4 x^2) theta(3 + x – 4 x^2) dx = -343/96~~-3.57292 |