Limits, Continuity & Differentiability · Polynomial satisfying a derivative identity

Let

f

be a real polynomial of degree

n

such that

f(x) = f'(x)\,f''(x)

, for all

x \in \mathbb{R}

. If

f(0) = 0

, then

36\left(f'(2) + f''(2) + \displaystyle\int_0^2 f(x)\,dx\right)

is equal to:

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