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Please help with the following proof:

Let $f(x)$ be a polynomial of degree n in $P_n(\mathbb{R})$. Prove that for any $g(x)$ element of $P_n(\mathbb{R})$ there exist scalers $c_0,c_1,\ldots,c_n$ such that
$$g(x) = c_0f(x) + c_1f'(x) + c_2f''(x) + \cdots + c_nf^{(n)}(x)$$

  • 1
    Try to prove that the set $\{ f(x),f'(x),\ldots,f^{(n)}(x) \}$ is linearly independent.2012-02-09

2 Answers 2