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QUESTION
Let h: [0 ,1] R be continuous. Prove that there exists w [0,1] such that h(w)= ((w + 1) / 2) h(0) + ((2w + 2) / 9) h(1/2) + ((w +1) /12) h(1) Hint:...
Let h: [0 ,1] → R be continuous.
Prove that there exists w ∈ [0,1] such that h(w)= ((w + 1) / 2) h(0) + ((2w + 2) / 9) h(1/2) + ((w +1) /12) h(1)
Hint: Consider H : [0 ,1]→R with H(w) = h(w) / (w +1)
