<s>[INST] $f(x) - f'(x) = x^3 + 3x^2 + 3x +1; f(9) =?$ Given the following $f(x) - f'(x) =  x^3 + 3x^2 + 3x +1$
Calculate $f(9) = ?$
I have tried to play with different number of derivatives. Also tried to solve it by equations.
Maybe there is some geometric meaning that could shade the light ?
I feel it is no complex problem at all.
Thanks for your solution
 [/INST] \begin{equation}
f(x) = ax^4 + bx^3 + cx^2 + dx + e\\f'(x) = 4ax^3 + 3bx^2 + 2cx + d\\f(x) - f'(x) = ax^4 + (b-4a)x^3 + (c-3b)x^2 + (d-2c)x + e - d = x^3 + 3x^2 + 3x +1\\a=0, b=1, c=6, d=15, e=16
\end{equation}
So, the function is $f(x)=x^3 + 6x^2 + 15x + 16$ and $f(9) = 1366$
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