If is a polynomial function satisfying and , , and then what is ?
Try this one as well: A Calculus problem 2
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The Limit tells us that the function f ( x ) must be a polynomial of degree 4 with leading coefficient 1 Since f ( 1 ) = 1 , f ( 2 ) = 2 , f ( 3 ) = 3 and f ( 4 ) = 4
f ( x ) = ( x − 1 ) ( x − 2 ) ( x − 3 ) ( x − 4 ) + x f ( 6 ) = 5 ! + 6 = 1 2 6