x(25-x)^3 - Wolfram|Alpha

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Input

x (25 - x)^3

Roots

x = 0

x = 25

Polynomial discriminant

Δ = 0

Derivative

d/dx(x (25 - x)^3) = (25 - 4 x) (25 - x)^2

Indefinite integral

integral x (25 - x)^3 dx = -x^5/5 + (75 x^4)/4 - 625 x^3 + (15625 x^2)/2 + constant

Global maximum

$max{x (25 - x)^3} = 10546875/256 at x = 25/4$

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