Hi,
1. The problem statement, all variables and given/known data
I am asked to show that P[x0,x1,...,xn] = 0 for P(x) [itex]\in[/itex]∏n-1 without directly using the property that the divided difference
over n+1 nodes is the nth derivative. The hint says to use the formula for the error.
2. Relevant equations
3. The attempt at a solution
I am not quite sure how to approach this. I am familiar with the expression for the error. I am also familiar with Rolle's Theorem, or Mean Value Theorem, but am I allowed/supposed to use that based on the indications in the question?
I'd appreciate some guidance. Thanks!
1. The problem statement, all variables and given/known data
I am asked to show that P[x0,x1,...,xn] = 0 for P(x) [itex]\in[/itex]∏n-1 without directly using the property that the divided difference
over n+1 nodes is the nth derivative. The hint says to use the formula for the error.
2. Relevant equations
3. The attempt at a solution
I am not quite sure how to approach this. I am familiar with the expression for the error. I am also familiar with Rolle's Theorem, or Mean Value Theorem, but am I allowed/supposed to use that based on the indications in the question?
I'd appreciate some guidance. Thanks!
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