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If f(x) is only known at the uniformly spaced grid points and a approximation to is desired at each, then what combination of differentiation rules could be used?

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If f(x) is only known at the uniformly spaced grid points<br><img src='https://www.fatskills.com/images2/GradExams/AA620223-18FE-45AA-A933-1A279C78DDA2.png' height='18' width='231'/> and a<br><img src='https://www.fatskills.com/images2/GradExams/7E42899F-ABFC-40B4-BCF5-4CFE6116DC9A.png' height='22' width='47'/> approximation to<br><img src='https://www.fatskills.com/images2/GradExams/327DDC3C-3077-4992-9247-BF89AEDCC1F3.png' height='22' width='47'/> is desired at each<br><img src='https://www.fatskills.com/images2/GradExams/015654E3-7CAD-484E-BCBB-A6FA011EF9AA.png' height='15' width='17'/>, then what combination of differentiation rules could be used?<br/>





 
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