Show that, if ∫(0 to 1)[(x^k)f(x)]dx=0 for k=0,1,…,n-1 and ∫(0 to 1)[(x^n)f(x)]dx=1 then |f(x_{0})|≥(2^n)n(n+1?
Let fєC([0,1]).Show that, if ∫(0 to 1)[(x^k)f(x)]dx=0 for k=0,1,…,n-1 and
∫(0 to 1)[(x^n)f(x)]dx=1 then |f(x_{0})|≥(2^n)n(n+1)
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What is f(x_{0}) supposed to mean?
Is it a typographical error for f(0) or we're supposed to show that there exists some point x_0 in [0,1] such that | f(x_0) | >= n * (n+1) * 2^n ?