Suppose that f is continuous on a, b Prove that given 0 there exist points x0 a x1 xn b such that if Ek y f(x) y for some x xk 1, xk , then sup Ek inf k for k 1,2, , n

Question: Suppose that f is continuous on [a, b]. Prove that given > 0 there exist points x0 = a < x1 <

Suppose that f is continuous on [a, b]. Prove that given ε > 0 there exist points x0 = a < x1 < ∙ ∙ ∙ < xn = b such that if Ek: = {y : f(x) = y for some x ∊ [xk-1, xk]}, then sup Ek - inf £k < ε for k = 1,2,..., n.

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