4x^2-x-3

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

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