4x^2-9

4x^2-9

Input
4 x^2 – 9
Geometric figure
parabola
Alternate form
(2 x – 3) (2 x + 3)
Polynomial discriminant
Delta = 144
Derivative
d/dx(4 x^2 – 9) = 8 x
Indefinite integral
integral (-9 + 4 x^2) dx = (4 x^3)/3 – 9 x + constant
Global minimum
min{4 x^2 – 9} = -9 at x = 0
Definite integral
integral_(-3/2)^(3/2) (-9 + 4 x^2) dx = -18
Definite integral area below the axis between the smallest and largest real roots
integral_(-3/2)^(3/2) (-9 + 4 x^2) theta(9 – 4 x^2) dx = -18

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