Application Of Derivatives

Let $f(x)=a_n x^n+a_{n-1} x^{n-1}+\cdots+a_1 x+a_0$ be a polynomial. Suppose that $f(0)=0$,

\(\left.\left.\frac{d f}{d x}\right]_{x=0}=1, \frac{d^2 f}{d x^2}\right]_{x=0}=4\)

and

\(\frac{d^3 f}{d x^3}=\frac{d^5 f}{d x^5}\)

Then $f(5)=$