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## Homework Statement

Find coefficients A, B, and C.

f'(x)= Af(x)+Bf(x+h)+Cf(x+2h)+O(h

^{2})

Using Taylor's Theorem.

Note: O stands for Big O in asymptotic order notation.

## The Attempt at a Solution

Here are the expansions:

Bf(x+h)= Bf(x)+Bhf'(x)+(1/2)Bh

^{2}f"(x)+(1/6)Bh

^{3}f"'(x)....

Cf(x+2h)=Cf(x)+2Chf'(x)+2Ch

^{2}f"(x)+(4/3)Ch

^{3}f"'(X)...

And then I added them and factored out the coefficients

= (A+B+C)f(x)+(B+2C)hf'(x)+(1/2B+2C)h

^{2}f"(x)+....

Is this correct? I'm stuck as to what I am supposed to do next.

Thanks.

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