A Polynomial from a Differential Identity

Difficulty: Hard · Topics: Algebra, Polynomials, Derivatives

Differensial ayniyatdan ko‘phad

Let F(x) be the antiderivative of the polynomial function f(x) whose coefficient of the highest term is 1 and satisfying the following

x≤ft\4x+d/dxF(x) \=-x^3+1/9\f'(x)\^2+xf(0)

for all real numbers x. If lim x→0fracf(x)x^2=3, find f(2).