4x-x^2

4x-x^2

Input
4 x – x^2
Geometric figure
parabola
Polynomial discriminant
Delta = 16
Derivative
d/dx(4 x – x^2) = 4 – 2 x
Indefinite integral
integral (4 x – x^2) dx = 2 x^2 – x^3/3 + constant
Global maximum
max{4 x – x^2} = 4 at x = 2
Definite integral
integral_0^4 (4 x – x^2) dx = 32/3~~10.6667
Definite integral area above the axis between the smallest and largest real roots
integral_0^4 (4 x – x^2) theta(4 x – x^2) dx = 32/3~~10.6667

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