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Means 2 a. Show that the point c guaranteed to exist by
Chapter 3, Problem 34AE(choose chapter or problem)
a. Show that the point o guaranteed to exist by the Mean Value Theorem for \(f(x)=x^{2}\) on [a, b] is the arithmetic mean of a and b; that is, c = (a + b) / 2.
b. Show that the point c guaranteed to exist by the Mean Value Theorem for f(x) = 1/x on [a, b], where 0 < a < b, is the geometric mean of a and b; that is, \(c=\sqrt{a b}\).
Questions & Answers
QUESTION:
a. Show that the point o guaranteed to exist by the Mean Value Theorem for \(f(x)=x^{2}\) on [a, b] is the arithmetic mean of a and b; that is, c = (a + b) / 2.
b. Show that the point c guaranteed to exist by the Mean Value Theorem for f(x) = 1/x on [a, b], where 0 < a < b, is the geometric mean of a and b; that is, \(c=\sqrt{a b}\).
ANSWER:Solution 34AE Step 1 In this problem we have to show that the poin