Suppose that f(x) is convex on an interval I. Show that f(x1) + f(x2) + ·+ f(xn) n for arbitrary n points x1, x2, ..., X, in I.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.4: Graphs Of Logarithmic Functions
Problem 60SE: Prove the conjecture made in the previous exercise.
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Suppose that f (x) is convex on an interval I. Show that
(X + x2 + + xn
f(x1) + f(x2) + ..+ f(xn)
n
n
for arbitrary n points x1, x2, .., X, in I.
Transcribed Image Text:Suppose that f (x) is convex on an interval I. Show that (X + x2 + + xn f(x1) + f(x2) + ..+ f(xn) n n for arbitrary n points x1, x2, .., X, in I.
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