Input
(x+3)^2 (x-2)^2
Plots
Alternate forms
x (x (x (x+2)-11)-12)+36
Expanded form
x^4+2 x^3-11 x^2-12 x+36
Roots
x = -3
Polynomial discriminant
Delta = 0
Properties as a real function
R (all real numbers)
Derivative
d/dx((x+3)^2 (x-2)^2) = 4 x^3+6 x^2-22 x-12
Indefinite integral
integral (-2+x)^2 (3+x)^2 dx = x^5/5+x^4/2-(11 x^3)/3-6 x^2+36 x+constant
Local maximum
max{(x+3)^2 (x-2)^2} = 625/16 at x = -1/2
Global minima
min{(x+3)^2 (x-2)^2} = 0 at x = 2
Definite integral
integral_(-3)^2 (-2+x)^2 (3+x)^2 dx = 625/6~~104.167
Definite integral area above the axis between the smallest and largest real roots
integral_(-3)^2 (-2+x)^2 (3+x)^2 theta((-2+x)^2 (3+x)^2) dx = 625/6~~104.167
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