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Suppose \(p_n(x)\) is a polynomial with degree \(n\) in the form of
a_0+a_1(x-c)+a_2(x-c)^2+\cdots+a_n(x-c)^n .
Find \(p_n(x)\) such that
f(c)=p_n(c), f^{\prime}(c)=p_n^{\prime}(c), f^{\prime \prime}(c)=p_n^{\prime \prime}(c), \ldots
in Mathematics by Platinum (141,884 points) | 23 views

1 Answer

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Best answer
We can take
a_k=\frac{f^{(k)}(c)}{k !}
f^{(k)}(c)=p_n^{(k)}(c)=k ! a_k .
by Platinum (141,884 points)

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