3x^2+5x-2

3x^2+5x-2

Input
3 x^2 + 5 x – 2
Geometric figure
parabola
Polynomial discriminant
Delta = 49
Derivative
d/dx(3 x^2 + 5 x – 2) = 6 x + 5
Indefinite integral
integral (-2 + 5 x + 3 x^2) dx = x^3 + (5 x^2)/2 – 2 x + constant
Global minimum
min{3 x^2 + 5 x – 2} = -49/12 at x = -5/6
Definite integral
integral_(-2)^(1/3) (-2 + 5 x + 3 x^2) dx = -343/54~~-6.35185
Definite integral area below the axis between the smallest and largest real roots
integral_(-2)^(1/3) (-2 + 5 x + 3 x^2) theta(2 – 5 x – 3 x^2) dx = -343/54~~-6.35185

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