Question: Let $f$ be a smooth function on $[1,2]$. Suppose that the following quadrature formula: $$ Vint_{1}^{2} f(x) d x approx a f(1)+ f(2)+c f^{prime) (2)
![Let $f$ be a smooth function on $[1,2]$. Suppose that the](https://dsd5zvtm8ll6.cloudfront.net/si.experts.images/questions/2024/09/66f9472952a2c_71366f9472906b93.jpg)
Let $f$ be a smooth function on $[1,2]$. Suppose that the following quadrature formula: $$ Vint_{1}^{2} f(x) d x \approx a f(1)+ f(2)+c f^{\prime) (2) $$ has the highest degree of precision, then the constants $a, b$ and $c$ are: $a=1 / 3, b=2 / 3, --1 / 6$ $a=1 / 2, b=1 / 2, C=-1 / 12$ $a=-1/2, b=3 / 2, C-1 / 6$ $a=5 / 6, b=1 / 6, c=1 / 3$ SP.SD.4531
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